{
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  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "using VMLS\n",
    "using LinearAlgebra"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Chapter 17\n",
    "# Constrained least squares applications\n",
    "### 17.1 Portfolio optimization\n",
    "**Compounded portfolio value.** The cumulative value of a portfolio from a return time series vector $r$, starting from the traditional value of $\\$10000$, is given by the value times series vector $v$, where \n",
    "\n",
    "$$\n",
    "v_t = 10000(1 + r_1) · · · (1 + r_{t−1}), t = 1, . . . , T. \n",
    "$$\n",
    "\n",
    "In other words, we form the *cumulative product* of the vector with entries $1 + r_t$. Julia has a built-in function that does this, `cumprod`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(11659.605992083187, 11505.476112955514)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Portfolio value with re-investment, return time series r\n",
    "cum_value(r) = 10000 * cumprod(1 .+ r)\n",
    "T = 250; # One year’s worth of trading days\n",
    "# Generate random returns sequence with\n",
    "# 10% annualized return, 5% annualized risk\n",
    "mu = 0.10/250; sigma = 0.05/sqrt(250);\n",
    "r = mu .+ sigma*randn(T);\n",
    "v = cum_value(r);\n",
    "# compare final value (compounded) and average return\n",
    "v[T] , v[1]*(1+sum(r))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The resulting figure for a particular choice of r is shown in Figure [17.1](#fig1)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
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      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using Plots\n",
    "plot(1:T, v, legend=false)\n",
    "plot!( xlabel = \"t\", ylabel = \"v_t\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Figure 17.1** <a ind=\"#fig1\"></a>Total portfolio value over time."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Portfolio optimization.** We define a function `port_opt` that evaluates the solution ([17.3](https://web.stanford.edu/~boyd/vmls/vmls.pdf#subsection.17.1.3)) of the constrained least squares problem ([17.2](https://web.stanford.edu/~boyd/vmls/vmls.pdf#equation.17.1.2)) in VMLS, and apply to the return data in VMLS Section [17.1.3](https://web.stanford.edu/~boyd/vmls/vmls.pdf#equation.17.1.3)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2000, 20)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function port_opt(R,rho)\n",
    "    T, n = size(R)\n",
    "    mu = sum(R, dims=1)'/T\n",
    "    KKT = [ 2*R'*R ones(n) mu; ones(n)' 0 0; mu' 0 0]\n",
    "    wz1z2 = KKT \\ [2*rho*T*mu; 1; rho]\n",
    "    w = wz1z2[1:n]\n",
    "    return w\n",
    "end;\n",
    "R, Rtest = portfolio_data();\n",
    "T, n = size(R)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.1"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rho = 0.10/250; # Ask for 10% annual return\n",
    "w = port_opt(R,rho);\n",
    "r = R*w; # Portfolio return time series\n",
    "pf_return = 250*avg(r)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0865018308685463"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pf_risk = sqrt(250)*stdev(r)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following produces the curve labeled “$10%$”. We also included the plots\n",
    "for $20%$ and $40%$ annual return, and for the $1/n$ portfolio $w = (1/n)1$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
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       "  784.213,1083.52 785.219,1083.13 786.225,1087.2 787.231,1090.51 788.237,1087.42 789.243,1090.25 790.249,1083.92 791.255,1080.23 792.262,1073.95 793.268,1066.72 \n",
       "  794.274,1066.31 795.28,1059.88 796.286,1063.47 797.292,1046.52 798.298,1039.61 799.305,1045.27 800.311,1041.51 801.317,1027.07 802.323,1025.37 803.329,1019.91 \n",
       "  804.335,1010.52 805.341,1018.14 806.348,1017.46 807.354,1013.01 808.36,989.77 809.366,988.546 810.372,977.991 811.378,983.217 812.384,984.229 813.391,994.464 \n",
       "  814.397,992.184 815.403,994.839 816.409,989.152 817.415,985.695 818.421,972.604 819.427,970.206 820.434,975.391 821.44,959.023 822.446,965.567 823.452,968.061 \n",
       "  824.458,957.764 825.464,975.676 826.47,974.075 827.477,969.123 828.483,967.685 829.489,965.895 830.495,975.108 831.501,968.203 832.507,966.77 833.513,968.736 \n",
       "  834.52,968.692 835.526,959.869 836.532,960.859 837.538,959.692 838.544,956.347 839.55,959.575 840.556,967.542 841.563,964.537 842.569,968.758 843.575,967.182 \n",
       "  844.581,972.454 845.587,972.948 846.593,964.412 847.599,970.399 848.606,964.315 849.612,957.021 850.618,953.641 851.624,960.434 852.63,957.059 853.636,957.653 \n",
       "  854.642,968.684 855.649,977.556 856.655,976.521 857.661,976.736 858.667,980.834 859.673,974.838 860.679,971.389 861.685,968.754 862.691,977.092 863.698,974.114 \n",
       "  864.704,983.91 865.71,996.973 866.716,999.028 867.722,995.104 868.728,994.921 869.734,996.191 870.741,996.09 871.747,990.718 872.753,979.899 873.759,982.764 \n",
       "  874.765,981.649 875.771,976.053 876.777,989.342 877.784,996.509 878.79,999.274 879.796,994.45 880.802,998.697 881.808,1009.15 882.814,1004.62 883.82,1009.25 \n",
       "  884.827,1011.35 885.833,1010.63 886.839,1005.05 887.845,995.172 888.851,1002.06 889.857,994.606 890.863,984.426 891.87,991.144 892.876,998.33 893.882,1000.37 \n",
       "  894.888,991.557 895.894,990.758 896.9,994.84 897.906,997.405 898.913,992.821 899.919,987.977 900.925,976.778 901.931,977.824 902.937,983.225 903.943,978.544 \n",
       "  904.949,975.375 905.956,978.304 906.962,978.353 907.968,977.219 908.974,987.091 909.98,1007.53 910.986,996.082 911.992,990.001 912.999,997.31 914.005,1002.28 \n",
       "  915.011,1007.94 916.017,1003.26 917.023,996.535 918.029,988.659 919.035,991.374 920.042,995.564 921.048,1006.34 922.054,1000.05 923.06,1006.32 924.066,1006.98 \n",
       "  925.072,996.493 926.078,1012.89 927.085,1009.06 928.091,1000.14 929.097,1006.26 930.103,1013.93 931.109,1011.09 932.115,1006.88 933.121,1014.13 934.127,1010.94 \n",
       "  935.134,1020.3 936.14,1013.75 937.146,1019.2 938.152,1024.14 939.158,1061.24 940.164,1055.3 941.17,1057.32 942.177,1058.34 943.183,1052.7 944.189,1046.68 \n",
       "  945.195,1046.05 946.201,1046.84 947.207,1055.6 948.213,1058.73 949.22,1065.85 950.226,1067.43 951.232,1072.33 952.238,1073.57 953.244,1070.13 954.25,1073.3 \n",
       "  955.256,1072.63 956.263,1070.26 957.269,1057.88 958.275,1062.56 959.281,1070.07 960.287,1069.08 961.293,1062.5 962.299,1053.73 963.306,1056.19 964.312,1056.2 \n",
       "  965.318,1053.12 966.324,1060.7 967.33,1051.94 968.336,1041.5 969.342,1044.31 970.349,1031.86 971.355,1021.77 972.361,1025.39 973.367,1036.03 974.373,1043.81 \n",
       "  975.379,1043.98 976.385,1053.1 977.392,1051.95 978.398,1043.27 979.404,1034.62 980.41,1040.99 981.416,1040.5 982.422,1040.67 983.428,1038.99 984.435,1020.32 \n",
       "  985.441,1019.83 986.447,1014.69 987.453,1021.38 988.459,1027.97 989.465,1021.27 990.471,1033.23 991.478,1022.38 992.484,1026.89 993.49,1013.69 994.496,1000.11 \n",
       "  995.502,1004.7 996.508,1009.41 997.514,1014.59 998.521,1020.79 999.527,1009.54 1000.53,1014.21 1001.54,1018.99 1002.55,1017.28 1003.55,1017.01 1004.56,1040.86 \n",
       "  1005.56,1034.61 1006.57,1031.84 1007.58,1027.31 1008.58,1024.01 1009.59,1023.47 1010.59,1026.84 1011.6,1028.26 1012.61,1021.08 1013.61,1022.58 1014.62,1022.48 \n",
       "  1015.62,1022.3 1016.63,1037.67 1017.64,1033.21 1018.64,1031.72 1019.65,1029.09 1020.66,1017.86 1021.66,996.306 1022.67,987.971 1023.67,989.673 1024.68,985.1 \n",
       "  1025.69,987.616 1026.69,995.053 1027.7,1002.41 1028.7,988.145 1029.71,995.789 1030.72,995.164 1031.72,999.174 1032.73,990.118 1033.74,989.815 1034.74,990.755 \n",
       "  1035.75,991.547 1036.75,990.478 1037.76,992.855 1038.77,993.031 1039.77,1001.76 1040.78,1000.04 1041.78,1006.65 1042.79,1007.43 1043.8,1001.11 1044.8,1004.08 \n",
       "  1045.81,997.451 1046.82,1001.72 1047.82,996.645 1048.83,977.896 1049.83,976.239 1050.84,981.823 1051.85,988.598 1052.85,987.079 1053.86,986.545 1054.86,989.795 \n",
       "  1055.87,994.668 1056.88,990.462 1057.88,977.742 1058.89,970.177 1059.9,969.178 1060.9,974.654 1061.91,979.322 1062.91,976.125 1063.92,975.691 1064.93,973.773 \n",
       "  1065.93,971.656 1066.94,971.762 1067.94,966.553 1068.95,958.075 1069.96,950.809 1070.96,942.339 1071.97,939.906 1072.97,941.773 1073.98,934.518 1074.99,932.87 \n",
       "  1075.99,938.723 1077,956.108 1078.01,947.48 1079.01,945.234 1080.02,950.802 1081.02,961.544 1082.03,951.809 1083.04,948.817 1084.04,948.455 1085.05,944.351 \n",
       "  1086.05,952.426 1087.06,944.997 1088.07,947.2 1089.07,938.794 1090.08,929.947 1091.09,931.904 1092.09,925.956 1093.1,921.895 1094.1,923.828 1095.11,924.876 \n",
       "  1096.12,923.739 1097.12,927.334 1098.13,932.283 1099.13,931.991 1100.14,925.245 1101.15,918.762 1102.15,918.694 1103.16,921.52 1104.17,920.239 1105.17,928.738 \n",
       "  1106.18,930.414 1107.18,935.094 1108.19,932.902 1109.2,941.738 1110.2,932.069 1111.21,933.048 1112.21,940.754 1113.22,939.463 1114.23,937.99 1115.23,934.273 \n",
       "  1116.24,929.436 1117.25,928.156 1118.25,928.578 1119.26,940.122 1120.26,948.926 1121.27,957.667 1122.28,957.681 1123.28,953.207 1124.29,955.168 1125.29,953.24 \n",
       "  1126.3,959.13 1127.31,945.789 1128.31,950.368 1129.32,949.841 1130.32,952.098 1131.33,958.021 1132.34,954.306 1133.34,955.17 1134.35,950.49 1135.36,943.776 \n",
       "  1136.36,945.831 1137.37,945.964 1138.37,943.592 1139.38,944.933 1140.39,941.895 1141.39,940.166 1142.4,938.958 1143.4,942.969 1144.41,943.3 1145.42,946.517 \n",
       "  1146.42,944.652 1147.43,955.031 1148.44,963.733 1149.44,961.133 1150.45,966.127 1151.45,968.341 1152.46,975.33 1153.47,984.922 1154.47,985.486 1155.48,981.17 \n",
       "  1156.48,984.915 1157.49,987.129 1158.5,988.273 1159.5,985.785 1160.51,984.864 1161.52,958.763 1162.52,963.127 1163.53,961.135 1164.53,958.551 1165.54,957.302 \n",
       "  1166.55,959.7 1167.55,952.978 1168.56,955.113 1169.56,967.362 1170.57,966.261 1171.58,971.346 1172.58,966.908 1173.59,971.565 1174.6,972.05 1175.6,956.944 \n",
       "  1176.61,956.783 1177.61,956.712 1178.62,956.06 1179.63,956.378 1180.63,959.364 1181.64,972.813 1182.64,981.039 1183.65,972.164 1184.66,972.969 1185.66,969.121 \n",
       "  1186.67,968.955 1187.67,976.036 1188.68,952.96 1189.69,951.838 1190.69,965.707 1191.7,983.838 1192.71,977.156 1193.71,976.067 1194.72,994.278 1195.72,1014.21 \n",
       "  1196.73,1006.54 1197.74,1011.11 1198.74,1015.39 1199.75,1009.17 1200.75,1006.56 1201.76,1006.59 1202.77,1007.84 1203.77,1010.13 1204.78,1019.3 1205.79,1006.69 \n",
       "  1206.79,1011.6 1207.8,1009.7 1208.8,1006.44 1209.81,1023.65 1210.82,1019.39 1211.82,1028.68 1212.83,1025.81 1213.83,1015.72 1214.84,1010.75 1215.85,990.76 \n",
       "  1216.85,985.925 1217.86,997.035 1218.87,975.77 1219.87,974.787 1220.88,978.373 1221.88,983.967 1222.89,980.442 1223.9,981.428 1224.9,975.063 1225.91,980.301 \n",
       "  1226.91,982.259 1227.92,976.931 1228.93,977.62 1229.93,972.205 1230.94,966.571 1231.95,956.463 1232.95,957.254 1233.96,948.855 1234.96,936.602 1235.97,938.986 \n",
       "  1236.98,926.839 1237.98,932.535 1238.99,928.531 1239.99,934.483 1241,935.806 1242.01,923.172 1243.01,915.492 1244.02,908.982 1245.03,918.769 1246.03,917.55 \n",
       "  1247.04,921.147 1248.04,915.719 1249.05,924.095 1250.06,919.902 1251.06,936.741 1252.07,942.994 1253.07,955.222 1254.08,956.883 1255.09,958.805 1256.09,935.766 \n",
       "  1257.1,935.906 1258.1,943.159 1259.11,932.201 1260.12,928.987 1261.12,916.277 1262.13,926.971 1263.14,928.479 1264.14,930.631 1265.15,927.566 1266.15,925.455 \n",
       "  1267.16,937.156 1268.17,925.798 1269.17,916.734 1270.18,920.275 1271.18,915.097 1272.19,909.585 1273.2,909.679 1274.2,913.828 1275.21,920.029 1276.22,917.824 \n",
       "  1277.22,920.297 1278.23,931.681 1279.23,930.098 1280.24,940.408 1281.25,938.322 1282.25,948.833 1283.26,949.398 1284.26,954.638 1285.27,939.926 1286.28,934.22 \n",
       "  1287.28,928.874 1288.29,931.719 1289.3,937.955 1290.3,938.2 1291.31,934.385 1292.31,939.557 1293.32,945.758 1294.33,946.776 1295.33,943.971 1296.34,926.422 \n",
       "  1297.34,922.246 1298.35,898.515 1299.36,918.739 1300.36,930.835 1301.37,954.17 1302.38,916.564 1303.38,914.781 1304.39,915.948 1305.39,914.641 1306.4,924.871 \n",
       "  1307.41,920.088 1308.41,929.673 1309.42,921.474 1310.42,923.971 1311.43,927.17 1312.44,915.815 1313.44,912.289 1314.45,912.491 1315.45,922.923 1316.46,929.152 \n",
       "  1317.47,917.874 1318.47,921.335 1319.48,919.018 1320.49,918.257 1321.49,913.152 1322.5,918.62 1323.5,910.312 1324.51,932.276 1325.52,923.757 1326.52,930.44 \n",
       "  1327.53,915.267 1328.53,913.14 1329.54,909.144 1330.55,918.109 1331.55,921.809 1332.56,936.372 1333.57,939.802 1334.57,935.886 1335.58,935.594 1336.58,946.297 \n",
       "  1337.59,963.844 1338.6,976.025 1339.6,977.708 1340.61,968.492 1341.61,962.452 1342.62,969.947 1343.63,982.234 1344.63,967.61 1345.64,971.784 1346.65,940.077 \n",
       "  1347.65,919.251 1348.66,912.195 1349.66,912.699 1350.67,905.9 1351.68,910.012 1352.68,895.046 1353.69,885.114 1354.69,894.088 1355.7,878.363 1356.71,881.352 \n",
       "  1357.71,885.562 1358.72,876.991 1359.73,885.85 1360.73,885.182 1361.74,885.897 1362.74,884.883 1363.75,881.367 1364.76,889.931 1365.76,882.222 1366.77,883.709 \n",
       "  1367.77,879.335 1368.78,887.258 1369.79,878.366 1370.79,889.157 1371.8,868.622 1372.8,873.473 1373.81,861.966 1374.82,867.477 1375.82,867.641 1376.83,876.817 \n",
       "  1377.84,874.133 1378.84,873.322 1379.85,879.572 1380.85,890.036 1381.86,886.089 1382.87,882.053 1383.87,879.594 1384.88,871.112 1385.88,877.78 1386.89,864.879 \n",
       "  1387.9,863.541 1388.9,868.225 1389.91,878.567 1390.92,872.334 1391.92,854.639 1392.93,842.396 1393.93,829.739 1394.94,821.276 1395.95,829.98 1396.95,840.875 \n",
       "  1397.96,847.862 1398.96,834.327 1399.97,812.33 1400.98,827.841 1401.98,824.982 1402.99,821.199 1404,827.154 1405,830.267 1406.01,817.353 1407.01,823.538 \n",
       "  1408.02,829.112 1409.03,822.422 1410.03,812.175 1411.04,819.618 1412.04,823.219 1413.05,826.171 1414.06,817.338 1415.06,847.066 1416.07,835.808 1417.08,838.913 \n",
       "  1418.08,828.545 1419.09,814.864 1420.09,815.024 1421.1,818.974 1422.11,805.48 1423.11,801.138 1424.12,827.898 1425.12,823.474 1426.13,814.577 1427.14,796.263 \n",
       "  1428.14,800.627 1429.15,840.315 1430.15,850.243 1431.16,877.691 1432.17,880.219 1433.17,898.62 1434.18,884.876 1435.19,893.428 1436.19,898.448 1437.2,892.789 \n",
       "  1438.2,891.747 1439.21,891.162 1440.22,891.861 1441.22,896.497 1442.23,878.618 1443.23,882.626 1444.24,899.065 1445.25,887.134 1446.25,878.625 1447.26,880.96 \n",
       "  1448.27,867.694 1449.27,865.736 1450.28,864.699 1451.28,863.954 1452.29,869.672 1453.3,873.14 1454.3,874.387 1455.31,870.894 1456.31,881.911 1457.32,889.668 \n",
       "  1458.33,887.357 1459.33,883.63 1460.34,886.539 1461.35,878.724 1462.35,871.886 1463.36,873.07 1464.36,878.109 1465.37,889.657 1466.38,881.436 1467.38,875.256 \n",
       "  1468.39,859.272 1469.39,872 1470.4,853.35 1471.41,858.232 1472.41,881.238 1473.42,859.634 1474.43,892.364 1475.43,905.908 1476.44,916.435 1477.44,922.001 \n",
       "  1478.45,892.993 1479.46,897.058 1480.46,906.801 1481.47,905.771 1482.47,913.391 1483.48,923.955 1484.49,928.144 1485.49,941.33 1486.5,924.189 1487.5,931.147 \n",
       "  1488.51,948.308 1489.52,962.099 1490.52,938.603 1491.53,951.549 1492.54,992.45 1493.54,963.5 1494.55,949.73 1495.55,934.618 1496.56,959.236 1497.57,985.348 \n",
       "  1498.57,1009.24 1499.58,1019.72 1500.58,1020.84 1501.59,965.439 1502.6,950.333 1503.6,916.287 1504.61,917.441 1505.62,924.467 1506.62,931.561 1507.63,951.191 \n",
       "  1508.63,961.777 1509.64,981.388 1510.65,998.243 1511.65,1004.26 1512.66,1030.47 1513.66,1000.32 1514.67,1020.06 1515.68,1017.4 1516.68,1032.04 1517.69,1031.79 \n",
       "  1518.7,1030.11 1519.7,998.66 1520.71,981.296 1521.71,966.276 1522.72,946.715 1523.73,945.312 1524.73,973.662 1525.74,960.453 1526.74,947.011 1527.75,925.814 \n",
       "  1528.76,907.328 1529.76,902.305 1530.77,932.286 1531.78,944.937 1532.78,953.745 1533.79,940.012 1534.79,948.562 1535.8,937.275 1536.81,914.188 1537.81,894.502 \n",
       "  1538.82,892.907 1539.82,915.161 1540.83,925.885 1541.84,925.703 1542.84,916.796 1543.85,922.225 1544.85,916.827 1545.86,904.098 1546.87,892.438 1547.87,895.227 \n",
       "  1548.88,908.914 1549.89,913.047 1550.89,910.692 1551.9,915.291 1552.9,898.758 1553.91,896.546 1554.92,914.135 1555.92,880.761 1556.93,866.006 1557.93,853.47 \n",
       "  1558.94,868.043 1559.95,833.274 1560.95,850.664 1561.96,858.167 1562.97,876.677 1563.97,861.017 1564.98,868.903 1565.98,862.387 1566.99,855.255 1568,829.042 \n",
       "  1569,845.974 1570.01,832.206 1571.01,847.387 1572.02,875.097 1573.03,880.231 1574.03,899.154 1575.04,867.679 1576.05,871.515 1577.05,874.755 1578.06,859.333 \n",
       "  1579.06,841.063 1580.07,834.926 1581.08,856.774 1582.08,856.298 1583.09,880.202 1584.09,896.64 1585.1,856.246 1586.11,872.064 1587.11,873.127 1588.12,860.713 \n",
       "  1589.13,863.184 1590.13,864.937 1591.14,911.824 1592.14,916.151 1593.15,913.847 1594.16,901.295 1595.16,884.753 1596.17,896.063 1597.17,879.912 1598.18,895.175 \n",
       "  1599.19,874.839 1600.19,868.858 1601.2,859.697 1602.21,874.302 1603.21,875.693 1604.22,858.477 1605.22,863.215 1606.23,852.782 1607.24,875.788 1608.24,873.672 \n",
       "  1609.25,839.078 1610.25,834.497 1611.26,840.274 1612.27,848.813 1613.27,826.953 1614.28,850.326 1615.28,873.416 1616.29,893.787 1617.3,871.805 1618.3,868.023 \n",
       "  1619.31,853.104 1620.32,848.953 1621.32,858.55 1622.33,822.227 1623.33,819.885 1624.34,825.907 1625.35,825.728 1626.35,806.816 1627.36,828.751 1628.36,829.656 \n",
       "  1629.37,840.937 1630.38,838.213 1631.38,842.997 1632.39,865.975 1633.4,894.294 1634.4,887.683 1635.41,889.729 1636.41,896.249 1637.42,901.068 1638.43,899.363 \n",
       "  1639.43,891.803 1640.44,886.345 1641.44,873.671 1642.45,874.737 1643.46,863.095 1644.46,853.668 1645.47,835.403 1646.48,834.507 1647.48,832.117 1648.49,803.445 \n",
       "  1649.49,802.762 1650.5,817.257 1651.51,811.926 1652.51,820.253 1653.52,823.533 1654.52,825.295 1655.53,820.819 1656.54,836.686 1657.54,860.285 1658.55,862.248 \n",
       "  1659.56,865.648 1660.56,867.554 1661.57,862.669 1662.57,852.719 1663.58,854.723 1664.59,854.649 1665.59,862.626 1666.6,869.92 1667.6,866.835 1668.61,876.698 \n",
       "  1669.62,876.18 1670.62,892.629 1671.63,892.994 1672.63,905.511 1673.64,883.831 1674.65,898.74 1675.65,888.072 1676.66,884.789 1677.67,889.825 1678.67,892.602 \n",
       "  1679.68,892.929 1680.68,890.756 1681.69,890.297 1682.7,894.692 1683.7,880.582 1684.71,889.398 1685.71,866.258 1686.72,890.255 1687.73,877.474 1688.73,888.681 \n",
       "  1689.74,889.626 1690.75,881.538 1691.75,868.785 1692.76,874.207 1693.76,880.944 1694.77,876.376 1695.78,885.756 1696.78,887.494 1697.79,864.293 1698.79,868.19 \n",
       "  1699.8,869.138 1700.81,862.231 1701.81,871.145 1702.82,880.632 1703.83,889.198 1704.83,889.614 1705.84,878.964 1706.84,877.337 1707.85,883.473 1708.86,886.594 \n",
       "  1709.86,890.48 1710.87,882.185 1711.87,871.458 1712.88,884.802 1713.89,893.626 1714.89,892.833 1715.9,897.772 1716.91,882.407 1717.91,876.526 1718.92,860.121 \n",
       "  1719.92,854.768 1720.93,856.507 1721.94,852.447 1722.94,849.44 1723.95,855.957 1724.95,847.225 1725.96,845.449 1726.97,838.109 1727.97,837.255 1728.98,841.521 \n",
       "  1729.98,846.078 1730.99,844.296 1732,835.735 1733,836.785 1734.01,828.345 1735.02,804.153 1736.02,818.851 1737.03,820.206 1738.03,815.987 1739.04,812.564 \n",
       "  1740.05,813.896 1741.05,824.539 1742.06,832.58 1743.06,839.174 1744.07,838.681 1745.08,840.639 1746.08,835.402 1747.09,825.38 1748.1,816.329 1749.1,824.022 \n",
       "  1750.11,825.539 1751.11,825.547 1752.12,845.679 1753.13,841.799 1754.13,842.613 1755.14,833.221 1756.14,822.372 1757.15,827.809 1758.16,819.707 1759.16,814.563 \n",
       "  1760.17,818.728 1761.18,801.18 1762.18,790.662 1763.19,786.422 1764.19,787.959 1765.2,788.711 1766.21,785.198 1767.21,778.383 1768.22,766.717 1769.22,776.344 \n",
       "  1770.23,784.49 1771.24,780.68 1772.24,777.509 1773.25,770.946 1774.26,768.412 1775.26,756.106 1776.27,758.902 1777.27,759.814 1778.28,764.358 1779.29,760.671 \n",
       "  1780.29,780.005 1781.3,788.181 1782.3,780.73 1783.31,778.034 1784.32,786.766 1785.32,770.045 1786.33,765.948 1787.33,762.224 1788.34,758.196 1789.35,754.785 \n",
       "  1790.35,759.045 1791.36,750.045 1792.37,753.211 1793.37,746.321 1794.38,744.155 1795.38,746.342 1796.39,748.991 1797.4,748.743 1798.4,749.47 1799.41,752.56 \n",
       "  1800.41,768.242 1801.42,764.726 1802.43,772.354 1803.43,770.247 1804.44,779.47 1805.45,784.094 1806.45,779.352 1807.46,778.387 1808.46,796.117 1809.47,791.754 \n",
       "  1810.48,791.05 1811.48,800.594 1812.49,789.744 1813.49,787.352 1814.5,791.039 1815.51,786.18 1816.51,795.688 1817.52,817.887 1818.53,815.279 1819.53,808.861 \n",
       "  1820.54,807.022 1821.54,810.663 1822.55,820.992 1823.56,829.752 1824.56,829.354 1825.57,819.068 1826.57,816.734 1827.58,814.326 1828.59,812.095 1829.59,807.066 \n",
       "  1830.6,802.973 1831.61,808.49 1832.61,810.489 1833.62,819.971 1834.62,818.252 1835.63,817.648 1836.64,821.518 1837.64,820.405 1838.65,822.39 1839.65,809 \n",
       "  1840.66,811.595 1841.67,805.18 1842.67,806.296 1843.68,809.605 1844.68,812.104 1845.69,806.451 1846.7,801.594 1847.7,798.54 1848.71,794.071 1849.72,795.04 \n",
       "  1850.72,795.968 1851.73,777.038 1852.73,774.646 1853.74,771.52 1854.75,774.716 1855.75,785.905 1856.76,782.373 1857.76,781.134 1858.77,781.822 1859.78,786.995 \n",
       "  1860.78,785.168 1861.79,778.263 1862.8,773.216 1863.8,775.055 1864.81,778.622 1865.81,776.618 1866.82,774.557 1867.83,776.694 1868.83,777.107 1869.84,787.368 \n",
       "  1870.84,801.253 1871.85,796.942 1872.86,792.8 1873.86,792.65 1874.87,792.243 1875.88,788.036 1876.88,794.229 1877.89,794.02 1878.89,802.818 1879.9,800.949 \n",
       "  1880.91,797.206 1881.91,803.367 1882.92,793.437 1883.92,791.021 1884.93,792.99 1885.94,804.007 1886.94,803.41 1887.95,789.666 1888.96,786.185 1889.96,783.202 \n",
       "  1890.97,782.774 1891.97,787.701 1892.98,780.5 1893.99,781.561 1894.99,785.98 1896,788.283 1897,780.876 1898.01,780.01 1899.02,777.622 1900.02,779.518 \n",
       "  1901.03,768.666 1902.03,761.658 1903.04,763.645 1904.05,745.208 1905.05,746.091 1906.06,759.828 1907.07,759.509 1908.07,748.79 1909.08,738.133 1910.08,729.586 \n",
       "  1911.09,731.74 1912.1,731.718 1913.1,720.886 1914.11,725.638 1915.11,719.373 1916.12,722.033 1917.13,719.702 1918.13,724.127 1919.14,717.239 1920.15,732.547 \n",
       "  1921.15,727.176 1922.16,731.918 1923.16,745.942 1924.17,756.136 1925.18,748.359 1926.18,744.628 1927.19,762.453 1928.19,763.731 1929.2,742.055 1930.21,742.577 \n",
       "  1931.21,747.77 1932.22,742.529 1933.23,749.461 1934.23,748.298 1935.24,742.03 1936.24,738.845 1937.25,735.727 1938.26,737.117 1939.26,724.258 1940.27,709.27 \n",
       "  1941.27,713.591 1942.28,702.949 1943.29,706.27 1944.29,702.835 1945.3,696.423 1946.31,704.317 1947.31,708.14 1948.32,697.805 1949.32,698.893 1950.33,698.61 \n",
       "  1951.34,692.947 1952.34,676.524 1953.35,687.438 1954.35,670.532 1955.36,683.026 1956.37,689.135 1957.37,678.79 1958.38,680.304 1959.39,683.454 1960.39,676.78 \n",
       "  1961.4,677.372 1962.4,675.627 1963.41,663.705 1964.42,655.77 1965.42,649.519 1966.43,643.748 1967.43,639.937 1968.44,626.489 1969.45,613.227 1970.45,611.679 \n",
       "  1971.46,600.914 1972.46,596.961 1973.47,595.099 1974.48,594.324 1975.48,603.561 1976.49,599.89 1977.5,590.292 1978.5,595.617 1979.51,590.998 1980.51,581.299 \n",
       "  1981.52,580.448 1982.53,578.807 1983.53,574.468 1984.54,563.971 1985.54,557.62 1986.55,547.996 1987.56,549.835 1988.56,549.543 1989.57,552.569 1990.58,550.579 \n",
       "  1991.58,549.602 1992.59,554.406 1993.59,558.901 1994.6,556.452 1995.61,554.888 1996.61,555.871 1997.62,550.258 1998.62,542.669 1999.63,536.59 2000.64,544.45 \n",
       "  2001.64,541.864 2002.65,540.239 2003.66,533.149 2004.66,529.146 2005.67,526.354 2006.67,530.149 2007.68,527.518 2008.69,516.292 2009.69,501.793 2010.7,505.445 \n",
       "  2011.7,498.346 2012.71,506.769 2013.72,491.639 2014.72,484.89 2015.73,497.258 2016.74,499.808 2017.74,501.697 2018.75,454.847 2019.75,458.453 2020.76,452.676 \n",
       "  2021.77,455.274 2022.77,435.888 2023.78,425.83 2024.78,403.627 2025.79,396.604 2026.8,394.047 2027.8,381.403 2028.81,390.073 2029.81,400.327 2030.82,387.06 \n",
       "  2031.83,373.284 2032.83,364.556 2033.84,371.004 2034.85,373.623 2035.85,364.697 2036.86,370.372 2037.86,373.174 2038.87,370.165 2039.88,362.894 2040.88,361.786 \n",
       "  2041.89,363.938 2042.89,360.985 2043.9,358.864 2044.91,360.008 2045.91,346.756 2046.92,371.361 2047.93,376.88 2048.93,388.738 2049.94,387.622 2050.94,388.894 \n",
       "  2051.95,387.022 2052.96,391.854 2053.96,386.722 2054.97,402.258 2055.97,398.521 2056.98,408.157 2057.99,406.312 2058.99,404.934 2060,418.132 2061.01,428.176 \n",
       "  2062.01,425.308 2063.02,413.181 2064.02,408.484 2065.03,405.72 2066.04,413.244 2067.04,408.989 2068.05,411.648 2069.05,414.443 2070.06,413.82 2071.07,407.479 \n",
       "  2072.07,421.881 2073.08,420.732 2074.09,410.152 2075.09,424.519 2076.1,417.124 2077.1,404.367 2078.11,407.297 2079.12,393.96 2080.12,390.024 2081.13,344.383 \n",
       "  2082.13,342.37 2083.14,348.248 2084.15,346.075 2085.15,343.709 2086.16,346.744 2087.16,332.769 2088.17,348.955 2089.18,357.822 2090.18,351.753 2091.19,343.028 \n",
       "  2092.2,327.961 2093.2,339.808 2094.21,345.305 2095.21,329.729 2096.22,327.385 2097.23,328.209 2098.23,323.12 2099.24,322.772 2100.24,298.483 2101.25,321.819 \n",
       "  2102.26,333.767 2103.26,323.158 2104.27,337.962 2105.28,321.363 2106.28,355.625 2107.29,355.965 2108.29,364.385 2109.3,349.06 2110.31,328.05 2111.31,331.93 \n",
       "  2112.32,334.95 2113.32,325.226 2114.33,315.811 2115.34,313.627 2116.34,298.175 2117.35,301.526 2118.36,307.932 2119.36,316.472 2120.37,310.111 2121.37,311.641 \n",
       "  2122.38,310.274 2123.39,307.356 2124.39,294.792 2125.4,285.229 2126.4,278.404 2127.41,271.686 2128.42,268.575 2129.42,269.508 2130.43,260.049 2131.44,276.607 \n",
       "  2132.44,289.168 2133.45,279.37 2134.45,283.97 2135.46,294.223 2136.47,286.551 2137.47,297.327 2138.48,299.028 2139.48,304.594 2140.49,299.046 2141.5,288.018 \n",
       "  2142.5,283.284 2143.51,299.888 2144.51,267.901 2145.52,254.927 2146.53,267.215 2147.53,266.449 2148.54,256.892 2149.55,239.825 2150.55,241.577 2151.56,245.814 \n",
       "  2152.56,243.023 2153.57,252.344 2154.58,242.879 2155.58,235.076 2156.59,237.955 2157.59,245.782 2158.6,253.543 2159.61,263.005 2160.61,263.566 2161.62,240.975 \n",
       "  2162.63,240.993 2163.63,242.922 2164.64,252.582 2165.64,253.521 2166.65,239.112 2167.66,248.536 2168.66,253.299 2169.67,242.305 2170.67,227.925 2171.68,224.601 \n",
       "  2172.69,229.97 2173.69,231.29 2174.7,224.42 2175.71,228.39 2176.71,181.572 2177.72,180.57 2178.72,178.034 2179.73,166.798 2180.74,157.711 2181.74,151.738 \n",
       "  2182.75,161.287 2183.75,157.968 2184.76,165.476 2185.77,170.483 2186.77,169.126 2187.78,170.979 2188.79,175.464 2189.79,176.734 2190.8,158.906 2191.8,165.075 \n",
       "  2192.81,168.923 2193.82,171.644 2194.82,177.884 2195.83,161.514 2196.83,167.764 2197.84,166.341 2198.85,167.278 2199.85,171.761 2200.86,195.833 2201.86,173.496 \n",
       "  2202.87,195.035 2203.88,171.222 2204.88,193.432 2205.89,170.181 2206.9,197.408 2207.9,206.718 2208.91,195.668 2209.91,187.179 2210.92,180.633 2211.93,168.926 \n",
       "  2212.93,190.095 2213.94,205.125 2214.94,187.238 2215.95,144.553 2216.96,137.898 2217.96,170.419 2218.97,154.72 2219.98,157.471 2220.98,151.122 2221.99,149.511 \n",
       "  2222.99,144.635 2224,144.246 2225.01,140.917 2226.01,128.257 2227.02,136.742 2228.02,159.602 2229.03,162.024 2230.04,147.835 2231.04,136.364 2232.05,139.375 \n",
       "  2233.06,122.059 2234.06,104.44 2235.07,110.018 2236.07,107.614 2237.08,112.559 2238.09,112.527 2239.09,111.847 2240.1,96.8111 2241.1,98.6815 2242.11,112.083 \n",
       "  2243.12,118.994 2244.12,123.127 2245.13,119.985 2246.14,119.332 2247.14,144.366 2248.15,139.877 2249.15,124.587 2250.16,131.91 2251.17,129.757 2252.17,119.704 \n",
       "  2253.18,103.49 2254.18,106.752 2255.19,112.516 2256.2,128.797 2257.2,129.459 2258.21,108.854 2259.21,119.378 2260.22,135.785 2261.23,126.768 2262.23,129.924 \n",
       "  2263.24,130.52 2264.25,134.253 2265.25,130.12 2266.26,124.456 2267.26,113.222 2268.27,88.0053 2269.28,91.5006 2270.28,97.5785 2271.29,107.754 2272.29,117.779 \n",
       "  2273.3,113.707 2274.31,114.688 2275.31,112.419 2276.32,130.047 2277.33,139.268 2278.33,132.805 2279.34,127.206 2280.34,112.396 2281.35,116.222 2282.36,129.641 \n",
       "  2283.36,106.652 2284.37,88.7367 2285.37,100.8 2286.38,96.7628 2287.39,91.903 2288.39,100.122 2289.4,104.878 2290.41,113.316 2291.41,108.25 2292.42,101.664 \n",
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      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using Plots\n",
    "plot(1:T, cum_value(r), label= \"10%\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
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       "<polyline clip-path=\"url(#clip6000)\" style=\"stroke:#000000; stroke-width:4; stroke-opacity:1; fill:none\" points=\"\n",
       "  328.094,1293.17 358.464,1293.17 \n",
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       "<polyline clip-path=\"url(#clip6000)\" style=\"stroke:#000000; stroke-width:4; stroke-opacity:1; fill:none\" points=\"\n",
       "  328.094,1039.97 358.464,1039.97 \n",
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       "<polyline clip-path=\"url(#clip6000)\" style=\"stroke:#000000; stroke-width:4; stroke-opacity:1; fill:none\" points=\"\n",
       "  328.094,786.777 358.464,786.777 \n",
       "  \"/>\n",
       "<polyline clip-path=\"url(#clip6000)\" style=\"stroke:#000000; stroke-width:4; stroke-opacity:1; fill:none\" points=\"\n",
       "  328.094,533.581 358.464,533.581 \n",
       "  \"/>\n",
       "<polyline clip-path=\"url(#clip6000)\" style=\"stroke:#000000; stroke-width:4; stroke-opacity:1; fill:none\" points=\"\n",
       "  328.094,280.386 358.464,280.386 \n",
       "  \"/>\n",
       "<g clip-path=\"url(#clip6000)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:middle;\" transform=\"rotate(0, 384.44, 1541.47)\" x=\"384.44\" y=\"1541.47\">0</text>\n",
       "</g>\n",
       "<g clip-path=\"url(#clip6000)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:middle;\" transform=\"rotate(0, 862.194, 1541.47)\" x=\"862.194\" y=\"1541.47\">500</text>\n",
       "</g>\n",
       "<g clip-path=\"url(#clip6000)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:middle;\" transform=\"rotate(0, 1339.95, 1541.47)\" x=\"1339.95\" y=\"1541.47\">1000</text>\n",
       "</g>\n",
       "<g clip-path=\"url(#clip6000)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:middle;\" transform=\"rotate(0, 1817.7, 1541.47)\" x=\"1817.7\" y=\"1541.47\">1500</text>\n",
       "</g>\n",
       "<g clip-path=\"url(#clip6000)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:middle;\" transform=\"rotate(0, 2295.45, 1541.47)\" x=\"2295.45\" y=\"1541.47\">2000</text>\n",
       "</g>\n",
       "<g clip-path=\"url(#clip6000)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:start;\" transform=\"rotate(0, 107.046, 1316.9)\" x=\"107.046\" y=\"1316.9\">2.50×10</text>\n",
       "</g>\n",
       "<g clip-path=\"url(#clip6000)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:38px; text-anchor:start;\" transform=\"rotate(0, 282.349, 1289.48)\" x=\"282.349\" y=\"1289.48\">4</text>\n",
       "</g>\n",
       "<g clip-path=\"url(#clip6000)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:start;\" transform=\"rotate(0, 107.046, 1063.7)\" x=\"107.046\" y=\"1063.7\">5.00×10</text>\n",
       "</g>\n",
       "<g clip-path=\"url(#clip6000)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:38px; text-anchor:start;\" transform=\"rotate(0, 282.349, 1036.29)\" x=\"282.349\" y=\"1036.29\">4</text>\n",
       "</g>\n",
       "<g clip-path=\"url(#clip6000)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:start;\" transform=\"rotate(0, 107.046, 810.504)\" x=\"107.046\" y=\"810.504\">7.50×10</text>\n",
       "</g>\n",
       "<g clip-path=\"url(#clip6000)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:38px; text-anchor:start;\" transform=\"rotate(0, 282.349, 783.094)\" x=\"282.349\" y=\"783.094\">4</text>\n",
       "</g>\n",
       "<g clip-path=\"url(#clip6000)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:start;\" transform=\"rotate(0, 107.046, 557.309)\" x=\"107.046\" y=\"557.309\">1.00×10</text>\n",
       "</g>\n",
       "<g clip-path=\"url(#clip6000)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:38px; text-anchor:start;\" transform=\"rotate(0, 282.349, 529.898)\" x=\"282.349\" y=\"529.898\">5</text>\n",
       "</g>\n",
       "<g clip-path=\"url(#clip6000)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:start;\" transform=\"rotate(0, 107.046, 304.113)\" x=\"107.046\" y=\"304.113\">1.25×10</text>\n",
       "</g>\n",
       "<g clip-path=\"url(#clip6000)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:38px; text-anchor:start;\" transform=\"rotate(0, 282.349, 276.703)\" x=\"282.349\" y=\"276.703\">5</text>\n",
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       "  394.951,1443.88 395.906,1443.98 396.862,1443.99 397.817,1443.29 398.773,1443.25 399.728,1443.45 400.684,1443.42 401.639,1441.85 402.595,1441.25 403.55,1441.04 \n",
       "  404.506,1441.8 405.461,1440.34 406.417,1439.79 407.372,1439.96 408.328,1439.49 409.283,1438.81 410.239,1437.73 411.194,1438.54 412.15,1438.7 413.105,1437.93 \n",
       "  414.061,1437.89 415.016,1437.59 415.972,1437.59 416.927,1436.57 417.883,1436.2 418.838,1436.18 419.794,1436.1 420.749,1436.09 421.705,1435.96 422.66,1435.5 \n",
       "  423.616,1435.77 424.571,1435.72 425.527,1435.2 426.482,1434.56 427.438,1434.03 428.393,1433.83 429.349,1434.89 430.304,1434.98 431.26,1435.35 432.215,1435.74 \n",
       "  433.171,1435.56 434.126,1434.93 435.082,1434.57 436.037,1435.14 436.993,1435.42 437.948,1435.58 438.904,1436.52 439.86,1436.64 440.815,1435.8 441.771,1435.5 \n",
       "  442.726,1434.71 443.682,1434.89 444.637,1434.72 445.593,1434.34 446.548,1434.49 447.504,1434.2 448.459,1434.1 449.415,1434.4 450.37,1434.89 451.326,1434.72 \n",
       "  452.281,1434.57 453.237,1434.25 454.192,1434.17 455.148,1434.33 456.103,1434.21 457.059,1434.25 458.014,1435.45 458.97,1435.91 459.925,1435.82 460.881,1435.5 \n",
       "  461.836,1435.52 462.792,1435.44 463.747,1435.74 464.703,1435.86 465.658,1435.32 466.614,1436.46 467.569,1438.02 468.525,1437.96 469.48,1438.45 470.436,1438.57 \n",
       "  471.391,1438.25 472.347,1437.89 473.302,1438.52 474.258,1437.94 475.213,1438.14 476.169,1438.04 477.124,1437.61 478.08,1437.1 479.035,1436.53 479.991,1437.02 \n",
       "  480.946,1436.52 481.902,1436.43 482.857,1435.94 483.813,1435.76 484.768,1435.59 485.724,1436.37 486.679,1436.3 487.635,1435.73 488.59,1435.42 489.546,1435.12 \n",
       "  490.501,1434.97 491.457,1435.15 492.412,1434.98 493.368,1434.81 494.323,1435.08 495.279,1435.2 496.234,1435.12 497.19,1435.25 498.145,1434.97 499.101,1434.16 \n",
       "  500.056,1433.73 501.012,1433.95 501.967,1433.55 502.923,1433.01 503.878,1432.46 504.834,1432.67 505.789,1432.48 506.745,1433.38 507.701,1433.31 508.656,1433.37 \n",
       "  509.612,1433.05 510.567,1432.37 511.523,1432.36 512.478,1432 513.434,1431.84 514.389,1432.14 515.345,1432.33 516.3,1431.75 517.256,1432.33 518.211,1432.55 \n",
       "  519.167,1431.78 520.122,1431.55 521.078,1431.47 522.033,1432.12 522.989,1432.08 523.944,1432.09 524.9,1431.87 525.855,1432.15 526.811,1432.84 527.766,1432.23 \n",
       "  528.722,1431.47 529.677,1430.49 530.633,1430.05 531.588,1430.34 532.544,1429.7 533.499,1430.09 534.455,1429.7 535.41,1429.41 536.366,1428.25 537.321,1428.68 \n",
       "  538.277,1428.45 539.232,1428.39 540.188,1428.53 541.143,1429.27 542.099,1429.49 543.054,1429.06 544.01,1429.18 544.965,1428.74 545.921,1427.55 546.876,1427.32 \n",
       "  547.832,1427.86 548.787,1428.95 549.743,1429.3 550.698,1428.18 551.654,1427.76 552.609,1427.57 553.565,1427.24 554.52,1427.72 555.476,1427.69 556.431,1427.15 \n",
       "  557.387,1426.81 558.342,1426.59 559.298,1425.89 560.253,1425.99 561.209,1425.92 562.164,1425.8 563.12,1425.81 564.075,1425.43 565.031,1424.59 565.986,1424.84 \n",
       "  566.942,1424.74 567.897,1424.48 568.853,1424.14 569.808,1424.03 570.764,1423.94 571.719,1424.04 572.675,1423.64 573.63,1423 574.586,1421.9 575.542,1421.9 \n",
       "  576.497,1422.36 577.453,1421.85 578.408,1423.32 579.364,1423.31 580.319,1423.03 581.275,1422.33 582.23,1422.39 583.186,1422.58 584.141,1422.63 585.097,1422.26 \n",
       "  586.052,1422.08 587.008,1421.94 587.963,1422.63 588.919,1422.96 589.874,1422.62 590.83,1421.73 591.785,1421.71 592.741,1421.76 593.696,1421.96 594.652,1422.56 \n",
       "  595.607,1422.11 596.563,1422.46 597.518,1423 598.474,1421.81 599.429,1420.77 600.385,1420.57 601.34,1420.47 602.296,1419.93 603.251,1419.86 604.207,1419.02 \n",
       "  605.162,1418.13 606.118,1419.66 607.073,1420.03 608.029,1420.24 608.984,1419.37 609.94,1418.81 610.895,1419.03 611.851,1418.56 612.806,1418.48 613.762,1418.58 \n",
       "  614.717,1419.32 615.673,1417.56 616.628,1417.74 617.584,1418.17 618.539,1417.7 619.495,1418.13 620.45,1418.12 621.406,1417.27 622.361,1417.38 623.317,1417.71 \n",
       "  624.272,1417.91 625.228,1418.11 626.183,1417.96 627.139,1417.78 628.094,1418.08 629.05,1418.19 630.005,1418.78 630.961,1419.18 631.916,1419.84 632.872,1420.24 \n",
       "  633.827,1419.83 634.783,1418.4 635.738,1418.54 636.694,1420.68 637.649,1420.94 638.605,1421.24 639.56,1421.21 640.516,1421.05 641.471,1421.96 642.427,1421.7 \n",
       "  643.383,1421.7 644.338,1421.58 645.294,1421.65 646.249,1422.21 647.205,1421.9 648.16,1422.44 649.116,1423.23 650.071,1423.17 651.027,1423.4 651.982,1423.03 \n",
       "  652.938,1423.14 653.893,1423.06 654.849,1423.01 655.804,1423.11 656.76,1423.47 657.715,1423.85 658.671,1423.41 659.626,1422.3 660.582,1421.63 661.537,1422.09 \n",
       "  662.493,1421.86 663.448,1422.7 664.404,1422.91 665.359,1423.19 666.315,1422.89 667.27,1422.96 668.226,1423.43 669.181,1423.73 670.137,1423.38 671.092,1423.35 \n",
       "  672.048,1422.67 673.003,1423.15 673.959,1423.3 674.914,1423.95 675.87,1424.47 676.825,1424.83 677.781,1424.99 678.736,1424.63 679.692,1424.3 680.647,1424.12 \n",
       "  681.603,1423.62 682.558,1423.67 683.514,1424.12 684.469,1423.39 685.425,1423.03 686.38,1423.13 687.336,1423.83 688.291,1424.27 689.247,1424.81 690.202,1424.95 \n",
       "  691.158,1426.02 692.113,1425.93 693.069,1426.48 694.024,1426.12 694.98,1426.14 695.935,1426.7 696.891,1426.1 697.846,1427.4 698.802,1426.15 699.757,1426.04 \n",
       "  700.713,1425.75 701.668,1425.65 702.624,1425.55 703.579,1425.41 704.535,1425.23 705.49,1424.8 706.446,1425.16 707.401,1424.9 708.357,1424.79 709.312,1425.39 \n",
       "  710.268,1425.4 711.224,1425.96 712.179,1426.22 713.135,1425.98 714.09,1425.2 715.046,1423.95 716.001,1423.54 716.957,1423.7 717.912,1424.25 718.868,1424.76 \n",
       "  719.823,1424.48 720.779,1424.54 721.734,1424.47 722.69,1424.01 723.645,1423.95 724.601,1423.3 725.556,1423.19 726.512,1423.11 727.467,1423.13 728.423,1423.55 \n",
       "  729.378,1423.62 730.334,1423.05 731.289,1422.59 732.245,1422.72 733.2,1422.77 734.156,1422.89 735.111,1422.79 736.067,1422.86 737.022,1423.3 737.978,1423.51 \n",
       "  738.933,1423.63 739.889,1423.53 740.844,1424.31 741.8,1423.63 742.755,1424.19 743.711,1423.92 744.666,1423.67 745.622,1423.26 746.577,1423.66 747.533,1424.19 \n",
       "  748.488,1423.71 749.444,1423.8 750.399,1423.79 751.355,1424.02 752.31,1423.5 753.266,1423.26 754.221,1423.26 755.177,1423.73 756.132,1422.79 757.088,1422.02 \n",
       "  758.043,1420.82 758.999,1420.89 759.954,1421.27 760.91,1420.9 761.865,1420.42 762.821,1420.88 763.776,1421.74 764.732,1421.28 765.687,1420.98 766.643,1421.52 \n",
       "  767.598,1421.76 768.554,1421.76 769.509,1421.93 770.465,1421.33 771.42,1420.56 772.376,1420.25 773.331,1419.86 774.287,1420.75 775.242,1420.77 776.198,1420.37 \n",
       "  777.153,1420.03 778.109,1420.41 779.065,1420.34 780.02,1420.66 780.976,1420.44 781.931,1420.61 782.887,1420.93 783.842,1421.35 784.798,1421.09 785.753,1421.14 \n",
       "  786.709,1421.72 787.664,1421.61 788.62,1422.09 789.575,1421.55 790.531,1420.8 791.486,1419.9 792.442,1420.08 793.397,1420.41 794.353,1420.36 795.308,1420.53 \n",
       "  796.264,1419.36 797.219,1420.29 798.175,1420.42 799.13,1419.32 800.086,1418.64 801.041,1418.42 801.997,1418.05 802.952,1418.35 803.908,1418.18 804.863,1417.56 \n",
       "  805.819,1416.97 806.774,1416.29 807.73,1416.66 808.685,1416.07 809.641,1416.11 810.596,1416.04 811.552,1415.89 812.507,1416.94 813.463,1416.76 814.418,1416.18 \n",
       "  815.374,1416.2 816.329,1416.86 817.285,1415.69 818.24,1415.38 819.196,1414.58 820.151,1413.6 821.107,1413.82 822.062,1414.04 823.018,1415.48 823.973,1415.56 \n",
       "  824.929,1415.26 825.884,1414.89 826.84,1414.4 827.795,1413.15 828.751,1412.84 829.706,1413.28 830.662,1414.15 831.617,1414.04 832.573,1412.74 833.528,1413.07 \n",
       "  834.484,1413.29 835.439,1413.72 836.395,1413.26 837.35,1412.59 838.306,1412.12 839.261,1412.41 840.217,1412.94 841.172,1412.73 842.128,1412.63 843.083,1413.34 \n",
       "  844.039,1413.65 844.994,1414.28 845.95,1414.54 846.906,1413.88 847.861,1413.49 848.817,1413.38 849.772,1413.55 850.728,1414.25 851.683,1414.16 852.639,1413.82 \n",
       "  853.594,1413.4 854.55,1412.52 855.505,1412.99 856.461,1413.54 857.416,1414.26 858.372,1413.77 859.327,1414.09 860.283,1413.83 861.238,1413.77 862.194,1413.51 \n",
       "  863.149,1413.44 864.105,1413.4 865.06,1413.76 866.016,1414.05 866.971,1413.78 867.927,1414.03 868.882,1413.47 869.838,1413.15 870.793,1412.6 871.749,1411.97 \n",
       "  872.704,1411.93 873.66,1411.37 874.615,1411.69 875.571,1410.21 876.526,1409.6 877.482,1410.1 878.437,1409.77 879.393,1408.51 880.348,1408.36 881.304,1407.88 \n",
       "  882.259,1407.06 883.215,1407.73 884.17,1407.67 885.126,1407.28 886.081,1405.25 887.037,1405.14 887.992,1404.22 888.948,1404.67 889.903,1404.76 890.859,1405.66 \n",
       "  891.814,1405.46 892.77,1405.69 893.725,1405.19 894.681,1404.89 895.636,1403.75 896.592,1403.54 897.547,1403.99 898.503,1402.56 899.458,1403.13 900.414,1403.35 \n",
       "  901.369,1402.45 902.325,1404.01 903.28,1403.87 904.236,1403.44 905.191,1403.32 906.147,1403.16 907.102,1403.96 908.058,1403.36 909.013,1403.24 909.969,1403.41 \n",
       "  910.924,1403.4 911.88,1402.63 912.835,1402.72 913.791,1402.62 914.747,1402.33 915.702,1402.61 916.658,1403.3 917.613,1403.04 918.569,1403.41 919.524,1403.27 \n",
       "  920.48,1403.73 921.435,1403.78 922.391,1403.03 923.346,1403.55 924.302,1403.02 925.257,1402.38 926.213,1402.09 927.168,1402.68 928.124,1402.39 929.079,1402.44 \n",
       "  930.035,1403.4 930.99,1404.18 931.946,1404.09 932.901,1404.11 933.857,1404.47 934.812,1403.94 935.768,1403.64 936.723,1403.41 937.679,1404.14 938.634,1403.88 \n",
       "  939.59,1404.73 940.545,1405.88 941.501,1406.06 942.456,1405.71 943.412,1405.7 944.367,1405.81 945.323,1405.8 946.278,1405.33 947.234,1404.38 948.189,1404.63 \n",
       "  949.145,1404.54 950.1,1404.05 951.056,1405.21 952.011,1405.83 952.967,1406.08 953.922,1405.66 954.878,1406.03 955.833,1406.94 956.789,1406.54 957.744,1406.95 \n",
       "  958.7,1407.13 959.655,1407.07 960.611,1406.58 961.566,1405.72 962.522,1406.32 963.477,1405.67 964.433,1404.78 965.388,1405.37 966.344,1405.99 967.299,1406.17 \n",
       "  968.255,1405.4 969.21,1405.33 970.166,1405.69 971.121,1405.91 972.077,1405.51 973.032,1405.09 973.988,1404.11 974.943,1404.2 975.899,1404.67 976.854,1404.27 \n",
       "  977.81,1403.99 978.765,1404.24 979.721,1404.25 980.676,1404.15 981.632,1405.01 982.587,1406.8 983.543,1405.8 984.499,1405.27 985.454,1405.91 986.41,1406.34 \n",
       "  987.365,1406.83 988.321,1406.42 989.276,1405.84 990.232,1405.15 991.187,1405.39 992.143,1405.75 993.098,1406.69 994.054,1406.14 995.009,1406.69 995.965,1406.75 \n",
       "  996.92,1405.83 997.876,1407.27 998.831,1406.93 999.787,1406.15 1000.74,1406.69 1001.7,1407.36 1002.65,1407.11 1003.61,1406.74 1004.56,1407.38 1005.52,1407.1 \n",
       "  1006.48,1407.91 1007.43,1407.34 1008.39,1407.82 1009.34,1408.25 1010.3,1411.49 1011.25,1410.97 1012.21,1411.15 1013.16,1411.24 1014.12,1410.75 1015.07,1410.22 \n",
       "  1016.03,1410.16 1016.99,1410.23 1017.94,1411 1018.9,1411.27 1019.85,1411.89 1020.81,1412.03 1021.76,1412.46 1022.72,1412.57 1023.67,1412.27 1024.63,1412.55 \n",
       "  1025.59,1412.49 1026.54,1412.28 1027.5,1411.2 1028.45,1411.61 1029.41,1412.26 1030.36,1412.18 1031.32,1411.6 1032.27,1410.84 1033.23,1411.05 1034.18,1411.05 \n",
       "  1035.14,1410.78 1036.1,1411.44 1037.05,1410.68 1038.01,1409.77 1038.96,1410.01 1039.92,1408.92 1040.87,1408.04 1041.83,1408.36 1042.78,1409.29 1043.74,1409.97 \n",
       "  1044.7,1409.98 1045.65,1410.78 1046.61,1410.68 1047.56,1409.92 1048.52,1409.17 1049.47,1409.72 1050.43,1409.68 1051.38,1409.69 1052.34,1409.55 1053.3,1407.92 \n",
       "  1054.25,1407.87 1055.21,1407.42 1056.16,1408.01 1057.12,1408.58 1058.07,1408 1059.03,1409.04 1059.98,1408.1 1060.94,1408.49 1061.89,1407.34 1062.85,1406.15 \n",
       "  1063.81,1406.55 1064.76,1406.96 1065.72,1407.42 1066.67,1407.96 1067.63,1406.97 1068.58,1407.38 1069.54,1407.8 1070.49,1407.65 1071.45,1407.63 1072.41,1409.71 \n",
       "  1073.36,1409.16 1074.32,1408.92 1075.27,1408.53 1076.23,1408.24 1077.18,1408.19 1078.14,1408.49 1079.09,1408.61 1080.05,1407.98 1081,1408.11 1081.96,1408.1 \n",
       "  1082.92,1408.09 1083.87,1409.43 1084.83,1409.04 1085.78,1408.91 1086.74,1408.68 1087.69,1407.7 1088.65,1405.82 1089.6,1405.09 1090.56,1405.24 1091.52,1404.84 \n",
       "  1092.47,1405.06 1093.43,1405.71 1094.38,1406.35 1095.34,1405.1 1096.29,1405.77 1097.25,1405.72 1098.2,1406.07 1099.16,1405.28 1100.11,1405.25 1101.07,1405.33 \n",
       "  1102.03,1405.4 1102.98,1405.31 1103.94,1405.52 1104.89,1405.53 1105.85,1406.29 1106.8,1406.14 1107.76,1406.72 1108.71,1406.79 1109.67,1406.24 1110.63,1406.5 \n",
       "  1111.58,1405.92 1112.54,1406.29 1113.49,1405.85 1114.45,1404.21 1115.4,1404.06 1116.36,1404.55 1117.31,1405.14 1118.27,1405.01 1119.23,1404.96 1120.18,1405.25 \n",
       "  1121.14,1405.67 1122.09,1405.31 1123.05,1404.2 1124,1403.53 1124.96,1403.45 1125.91,1403.93 1126.87,1404.33 1127.82,1404.05 1128.78,1404.02 1129.74,1403.85 \n",
       "  1130.69,1403.66 1131.65,1403.67 1132.6,1403.22 1133.56,1402.48 1134.51,1401.84 1135.47,1401.1 1136.42,1400.89 1137.38,1401.05 1138.34,1400.42 1139.29,1400.27 \n",
       "  1140.25,1400.79 1141.2,1402.3 1142.16,1401.55 1143.11,1401.35 1144.07,1401.84 1145.02,1402.78 1145.98,1401.93 1146.93,1401.67 1147.89,1401.64 1148.85,1401.28 \n",
       "  1149.8,1401.98 1150.76,1401.33 1151.71,1401.53 1152.67,1400.79 1153.62,1400.02 1154.58,1400.19 1155.53,1399.67 1156.49,1399.31 1157.45,1399.48 1158.4,1399.58 \n",
       "  1159.36,1399.48 1160.31,1399.79 1161.27,1400.22 1162.22,1400.2 1163.18,1399.61 1164.13,1399.04 1165.09,1399.03 1166.04,1399.28 1167,1399.17 1167.96,1399.91 \n",
       "  1168.91,1400.06 1169.87,1400.47 1170.82,1400.28 1171.78,1401.05 1172.73,1400.2 1173.69,1400.29 1174.64,1400.96 1175.6,1400.85 1176.56,1400.72 1177.51,1400.4 \n",
       "  1178.47,1399.97 1179.42,1399.86 1180.38,1399.9 1181.33,1400.91 1182.29,1401.68 1183.24,1402.44 1184.2,1402.44 1185.15,1402.05 1186.11,1402.22 1187.07,1402.05 \n",
       "  1188.02,1402.57 1188.98,1401.4 1189.93,1401.8 1190.89,1401.76 1191.84,1401.95 1192.8,1402.47 1193.75,1402.15 1194.71,1402.22 1195.67,1401.81 1196.62,1401.23 \n",
       "  1197.58,1401.41 1198.53,1401.42 1199.49,1401.21 1200.44,1401.33 1201.4,1401.06 1202.35,1400.91 1203.31,1400.81 1204.27,1401.16 1205.22,1401.19 1206.18,1401.47 \n",
       "  1207.13,1401.3 1208.09,1402.21 1209.04,1402.97 1210,1402.74 1210.95,1403.18 1211.91,1403.37 1212.86,1403.98 1213.82,1404.82 1214.78,1404.87 1215.73,1404.49 \n",
       "  1216.69,1404.82 1217.64,1405.02 1218.6,1405.12 1219.55,1404.9 1220.51,1404.82 1221.46,1402.54 1222.42,1402.92 1223.38,1402.74 1224.33,1402.52 1225.29,1402.41 \n",
       "  1226.24,1402.62 1227.2,1402.03 1228.15,1402.22 1229.11,1403.29 1230.06,1403.19 1231.02,1403.64 1231.97,1403.25 1232.93,1403.66 1233.89,1403.7 1234.84,1402.38 \n",
       "  1235.8,1402.36 1236.75,1402.36 1237.71,1402.3 1238.66,1402.33 1239.62,1402.59 1240.57,1403.76 1241.53,1404.48 1242.49,1403.71 1243.44,1403.78 1244.4,1403.44 \n",
       "  1245.35,1403.43 1246.31,1404.05 1247.26,1402.03 1248.22,1401.93 1249.17,1403.14 1250.13,1404.73 1251.08,1404.14 1252.04,1404.05 1253,1405.64 1253.95,1407.38 \n",
       "  1254.91,1406.71 1255.86,1407.11 1256.82,1407.49 1257.77,1406.94 1258.73,1406.71 1259.68,1406.72 1260.64,1406.83 1261.6,1407.03 1262.55,1407.83 1263.51,1406.72 \n",
       "  1264.46,1407.15 1265.42,1406.99 1266.37,1406.7 1267.33,1408.21 1268.28,1407.83 1269.24,1408.65 1270.2,1408.4 1271.15,1407.51 1272.11,1407.08 1273.06,1405.33 \n",
       "  1274.02,1404.91 1274.97,1405.88 1275.93,1404.02 1276.88,1403.94 1277.84,1404.25 1278.79,1404.74 1279.75,1404.43 1280.71,1404.52 1281.66,1403.96 1282.62,1404.42 \n",
       "  1283.57,1404.59 1284.53,1404.12 1285.48,1404.18 1286.44,1403.71 1287.39,1403.22 1288.35,1402.34 1289.31,1402.4 1290.26,1401.67 1291.22,1400.6 1292.17,1400.81 \n",
       "  1293.13,1399.75 1294.08,1400.24 1295.04,1399.89 1295.99,1400.41 1296.95,1400.53 1297.9,1399.43 1298.86,1398.76 1299.82,1398.19 1300.77,1399.04 1301.73,1398.94 \n",
       "  1302.68,1399.25 1303.64,1398.77 1304.59,1399.51 1305.55,1399.14 1306.5,1400.61 1307.46,1401.16 1308.42,1402.23 1309.37,1402.37 1310.33,1402.54 1311.28,1400.53 \n",
       "  1312.24,1400.54 1313.19,1401.17 1314.15,1400.22 1315.1,1399.93 1316.06,1398.82 1317.01,1399.76 1317.97,1399.89 1318.93,1400.08 1319.88,1399.81 1320.84,1399.63 \n",
       "  1321.79,1400.65 1322.75,1399.66 1323.7,1398.86 1324.66,1399.17 1325.61,1398.72 1326.57,1398.24 1327.53,1398.25 1328.48,1398.61 1329.44,1399.15 1330.39,1398.96 \n",
       "  1331.35,1399.18 1332.3,1400.17 1333.26,1400.03 1334.21,1400.93 1335.17,1400.75 1336.13,1401.67 1337.08,1401.72 1338.04,1402.18 1338.99,1400.89 1339.95,1400.39 \n",
       "  1340.9,1399.92 1341.86,1400.17 1342.81,1400.72 1343.77,1400.74 1344.72,1400.41 1345.68,1400.86 1346.64,1401.4 1347.59,1401.49 1348.55,1401.24 1349.5,1399.71 \n",
       "  1350.46,1399.35 1351.41,1397.27 1352.37,1399.04 1353.32,1400.1 1354.28,1402.14 1355.24,1398.85 1356.19,1398.69 1357.15,1398.8 1358.1,1398.68 1359.06,1399.57 \n",
       "  1360.01,1399.16 1360.97,1399.99 1361.92,1399.28 1362.88,1399.5 1363.83,1399.78 1364.79,1398.78 1365.75,1398.48 1366.7,1398.49 1367.66,1399.4 1368.61,1399.95 \n",
       "  1369.57,1398.96 1370.52,1399.27 1371.48,1399.06 1372.43,1399 1373.39,1398.55 1374.35,1399.03 1375.3,1398.3 1376.26,1400.22 1377.21,1399.48 1378.17,1400.06 \n",
       "  1379.12,1398.74 1380.08,1398.55 1381.03,1398.2 1381.99,1398.98 1382.94,1399.31 1383.9,1400.58 1384.86,1400.88 1385.81,1400.54 1386.77,1400.51 1387.72,1401.45 \n",
       "  1388.68,1402.98 1389.63,1404.04 1390.59,1404.19 1391.54,1403.39 1392.5,1402.86 1393.46,1403.51 1394.41,1404.59 1395.37,1403.31 1396.32,1403.67 1397.28,1400.9 \n",
       "  1398.23,1399.08 1399.19,1398.47 1400.14,1398.51 1401.1,1397.92 1402.06,1398.28 1403.01,1396.97 1403.97,1396.1 1404.92,1396.88 1405.88,1395.51 1406.83,1395.77 \n",
       "  1407.79,1396.14 1408.74,1395.39 1409.7,1396.16 1410.65,1396.11 1411.61,1396.17 1412.57,1396.08 1413.52,1395.77 1414.48,1396.52 1415.43,1395.85 1416.39,1395.98 \n",
       "  1417.34,1395.6 1418.3,1396.29 1419.25,1395.51 1420.21,1396.45 1421.17,1394.66 1422.12,1395.08 1423.08,1394.08 1424.03,1394.56 1424.99,1394.57 1425.94,1395.38 \n",
       "  1426.9,1395.14 1427.85,1395.07 1428.81,1395.62 1429.76,1396.53 1430.72,1396.19 1431.68,1395.83 1432.63,1395.62 1433.59,1394.88 1434.54,1395.46 1435.5,1394.33 \n",
       "  1436.45,1394.22 1437.41,1394.62 1438.36,1395.53 1439.32,1394.98 1440.28,1393.44 1441.23,1392.37 1442.19,1391.26 1443.14,1390.52 1444.1,1391.28 1445.05,1392.23 \n",
       "  1446.01,1392.85 1446.96,1391.66 1447.92,1389.74 1448.87,1391.1 1449.83,1390.85 1450.79,1390.52 1451.74,1391.04 1452.7,1391.31 1453.65,1390.18 1454.61,1390.72 \n",
       "  1455.56,1391.21 1456.52,1390.62 1457.47,1389.73 1458.43,1390.38 1459.39,1390.69 1460.34,1390.95 1461.3,1390.18 1462.25,1392.78 1463.21,1391.79 1464.16,1392.06 \n",
       "  1465.12,1391.16 1466.07,1389.96 1467.03,1389.98 1467.99,1390.32 1468.94,1389.14 1469.9,1388.76 1470.85,1391.1 1471.81,1390.71 1472.76,1389.94 1473.72,1388.34 \n",
       "  1474.67,1388.72 1475.63,1392.19 1476.58,1393.05 1477.54,1395.45 1478.5,1395.67 1479.45,1397.28 1480.41,1396.08 1481.36,1396.83 1482.32,1397.27 1483.27,1396.77 \n",
       "  1484.23,1396.68 1485.18,1396.63 1486.14,1396.69 1487.1,1397.1 1488.05,1395.53 1489.01,1395.88 1489.96,1397.32 1490.92,1396.28 1491.87,1395.53 1492.83,1395.74 \n",
       "  1493.78,1394.58 1494.74,1394.41 1495.69,1394.32 1496.65,1394.25 1497.61,1394.75 1498.56,1395.05 1499.52,1395.16 1500.47,1394.86 1501.43,1395.82 1502.38,1396.5 \n",
       "  1503.34,1396.3 1504.29,1395.97 1505.25,1396.23 1506.21,1395.54 1507.16,1394.94 1508.12,1395.05 1509.07,1395.49 1510.03,1396.5 1510.98,1395.78 1511.94,1395.24 \n",
       "  1512.89,1393.84 1513.85,1394.95 1514.8,1393.32 1515.76,1393.75 1516.72,1395.76 1517.67,1393.87 1518.63,1396.73 1519.58,1397.92 1520.54,1398.84 1521.49,1399.32 \n",
       "  1522.45,1396.79 1523.4,1397.14 1524.36,1398 1525.32,1397.91 1526.27,1398.57 1527.23,1399.49 1528.18,1399.86 1529.14,1401.01 1530.09,1399.52 1531.05,1400.12 \n",
       "  1532,1401.62 1532.96,1402.83 1533.92,1400.77 1534.87,1401.91 1535.83,1405.48 1536.78,1402.95 1537.74,1401.75 1538.69,1400.43 1539.65,1402.58 1540.6,1404.86 \n",
       "  1541.56,1406.95 1542.51,1407.86 1543.47,1407.96 1544.43,1403.12 1545.38,1401.8 1546.34,1398.82 1547.29,1398.93 1548.25,1399.54 1549.2,1400.16 1550.16,1401.87 \n",
       "  1551.11,1402.8 1552.07,1404.51 1553.03,1405.99 1553.98,1406.51 1554.94,1408.8 1555.89,1406.17 1556.85,1407.89 1557.8,1407.66 1558.76,1408.94 1559.71,1408.92 \n",
       "  1560.67,1408.77 1561.62,1406.02 1562.58,1404.51 1563.54,1403.19 1564.49,1401.48 1565.45,1401.36 1566.4,1403.84 1567.36,1402.68 1568.31,1401.51 1569.27,1399.66 \n",
       "  1570.22,1398.04 1571.18,1397.6 1572.14,1400.22 1573.09,1401.33 1574.05,1402.1 1575,1400.9 1575.96,1401.65 1576.91,1400.66 1577.87,1398.64 1578.82,1396.92 \n",
       "  1579.78,1396.78 1580.73,1398.73 1581.69,1399.66 1582.65,1399.65 1583.6,1398.87 1584.56,1399.34 1585.51,1398.87 1586.47,1397.76 1587.42,1396.74 1588.38,1396.98 \n",
       "  1589.33,1398.18 1590.29,1398.54 1591.25,1398.34 1592.2,1398.74 1593.16,1397.29 1594.11,1397.1 1595.07,1398.64 1596.02,1395.72 1596.98,1394.43 1597.93,1393.34 \n",
       "  1598.89,1394.61 1599.85,1391.57 1600.8,1393.09 1601.76,1393.75 1602.71,1395.36 1603.67,1393.99 1604.62,1394.68 1605.58,1394.11 1606.53,1393.49 1607.49,1391.2 \n",
       "  1608.44,1392.68 1609.4,1391.48 1610.36,1392.8 1611.31,1395.23 1612.27,1395.67 1613.22,1397.33 1614.18,1394.58 1615.13,1394.91 1616.09,1395.2 1617.04,1393.85 \n",
       "  1618,1392.25 1618.96,1391.71 1619.91,1393.62 1620.87,1393.58 1621.82,1395.67 1622.78,1397.11 1623.73,1393.58 1624.69,1394.96 1625.64,1395.05 1626.6,1393.97 \n",
       "  1627.55,1394.18 1628.51,1394.34 1629.47,1398.43 1630.42,1398.81 1631.38,1398.61 1632.33,1397.51 1633.29,1396.07 1634.24,1397.06 1635.2,1395.65 1636.15,1396.98 \n",
       "  1637.11,1395.2 1638.07,1394.68 1639.02,1393.88 1639.98,1395.16 1640.93,1395.28 1641.89,1393.77 1642.84,1394.19 1643.8,1393.28 1644.75,1395.29 1645.71,1395.1 \n",
       "  1646.66,1392.08 1647.62,1391.68 1648.58,1392.18 1649.53,1392.93 1650.49,1391.02 1651.44,1393.06 1652.4,1395.08 1653.35,1396.86 1654.31,1394.94 1655.26,1394.61 \n",
       "  1656.22,1393.3 1657.18,1392.94 1658.13,1393.78 1659.09,1390.61 1660.04,1390.4 1661,1390.93 1661.95,1390.91 1662.91,1389.26 1663.86,1391.18 1664.82,1391.25 \n",
       "  1665.78,1392.24 1666.73,1392 1667.69,1392.42 1668.64,1394.43 1669.6,1396.9 1670.55,1396.33 1671.51,1396.5 1672.46,1397.07 1673.42,1397.49 1674.37,1397.35 \n",
       "  1675.33,1396.69 1676.29,1396.21 1677.24,1395.1 1678.2,1395.19 1679.15,1394.18 1680.11,1393.35 1681.06,1391.76 1682.02,1391.68 1682.97,1391.47 1683.93,1388.96 \n",
       "  1684.89,1388.9 1685.84,1390.17 1686.8,1389.7 1687.75,1390.43 1688.71,1390.72 1689.66,1390.87 1690.62,1390.48 1691.57,1391.87 1692.53,1393.93 1693.48,1394.1 \n",
       "  1694.44,1394.4 1695.4,1394.57 1696.35,1394.14 1697.31,1393.27 1698.26,1393.44 1699.22,1393.44 1700.17,1394.14 1701.13,1394.77 1702.08,1394.5 1703.04,1395.37 \n",
       "  1704,1395.32 1704.95,1396.76 1705.91,1396.79 1706.86,1397.88 1707.82,1395.99 1708.77,1397.29 1709.73,1396.36 1710.68,1396.07 1711.64,1396.51 1712.59,1396.75 \n",
       "  1713.55,1396.78 1714.51,1396.59 1715.46,1396.55 1716.42,1396.94 1717.37,1395.7 1718.33,1396.47 1719.28,1394.45 1720.24,1396.55 1721.19,1395.43 1722.15,1396.41 \n",
       "  1723.11,1396.49 1724.06,1395.79 1725.02,1394.67 1725.97,1395.15 1726.93,1395.74 1727.88,1395.34 1728.84,1396.16 1729.79,1396.31 1730.75,1394.28 1731.71,1394.62 \n",
       "  1732.66,1394.7 1733.62,1394.1 1734.57,1394.88 1735.53,1395.71 1736.48,1396.46 1737.44,1396.49 1738.39,1395.56 1739.35,1395.42 1740.3,1395.96 1741.26,1396.23 \n",
       "  1742.22,1396.57 1743.17,1395.84 1744.13,1394.91 1745.08,1396.07 1746.04,1396.84 1746.99,1396.78 1747.95,1397.21 1748.9,1395.86 1749.86,1395.35 1750.82,1393.92 \n",
       "  1751.77,1393.45 1752.73,1393.6 1753.68,1393.25 1754.64,1392.98 1755.59,1393.55 1756.55,1392.79 1757.5,1392.63 1758.46,1391.99 1759.41,1391.92 1760.37,1392.29 \n",
       "  1761.33,1392.69 1762.28,1392.53 1763.24,1391.79 1764.19,1391.88 1765.15,1391.14 1766.1,1389.03 1767.06,1390.31 1768.01,1390.43 1768.97,1390.06 1769.93,1389.76 \n",
       "  1770.88,1389.88 1771.84,1390.81 1772.79,1391.51 1773.75,1392.09 1774.7,1392.04 1775.66,1392.21 1776.61,1391.76 1777.57,1390.88 1778.52,1390.09 1779.48,1390.76 \n",
       "  1780.44,1390.89 1781.39,1390.9 1782.35,1392.65 1783.3,1392.32 1784.26,1392.39 1785.21,1391.57 1786.17,1390.62 1787.12,1391.09 1788.08,1390.38 1789.04,1389.94 \n",
       "  1789.99,1390.3 1790.95,1388.77 1791.9,1387.85 1792.86,1387.48 1793.81,1387.61 1794.77,1387.68 1795.72,1387.37 1796.68,1386.77 1797.63,1385.75 1798.59,1386.6 \n",
       "  1799.55,1387.31 1800.5,1386.97 1801.46,1386.7 1802.41,1386.12 1803.37,1385.9 1804.32,1384.83 1805.28,1385.07 1806.23,1385.15 1807.19,1385.55 1808.15,1385.23 \n",
       "  1809.1,1386.92 1810.06,1387.63 1811.01,1386.98 1811.97,1386.74 1812.92,1387.51 1813.88,1386.05 1814.83,1385.69 1815.79,1385.36 1816.75,1385.01 1817.7,1384.71 \n",
       "  1818.66,1385.08 1819.61,1384.3 1820.57,1384.57 1821.52,1383.97 1822.48,1383.78 1823.43,1383.97 1824.39,1384.21 1825.34,1384.18 1826.3,1384.25 1827.26,1384.52 \n",
       "  1828.21,1385.89 1829.17,1385.58 1830.12,1386.25 1831.08,1386.06 1832.03,1386.87 1832.99,1387.27 1833.94,1386.86 1834.9,1386.77 1835.86,1388.32 1836.81,1387.94 \n",
       "  1837.77,1387.88 1838.72,1388.71 1839.68,1387.77 1840.63,1387.56 1841.59,1387.88 1842.54,1387.46 1843.5,1388.29 1844.45,1390.23 1845.41,1390 1846.37,1389.44 \n",
       "  1847.32,1389.28 1848.28,1389.59 1849.23,1390.5 1850.19,1391.26 1851.14,1391.23 1852.1,1390.33 1853.05,1390.13 1854.01,1389.91 1854.97,1389.72 1855.92,1389.28 \n",
       "  1856.88,1388.92 1857.83,1389.4 1858.79,1389.58 1859.74,1390.41 1860.7,1390.26 1861.65,1390.2 1862.61,1390.54 1863.56,1390.45 1864.52,1390.62 1865.48,1389.45 \n",
       "  1866.43,1389.68 1867.39,1389.12 1868.34,1389.21 1869.3,1389.5 1870.25,1389.72 1871.21,1389.23 1872.16,1388.8 1873.12,1388.54 1874.08,1388.14 1875.03,1388.23 \n",
       "  1875.99,1388.31 1876.94,1386.66 1877.9,1386.45 1878.85,1386.17 1879.81,1386.45 1880.76,1387.43 1881.72,1387.12 1882.68,1387.01 1883.63,1387.07 1884.59,1387.53 \n",
       "  1885.54,1387.37 1886.5,1386.76 1887.45,1386.32 1888.41,1386.48 1889.36,1386.79 1890.32,1386.62 1891.27,1386.44 1892.23,1386.63 1893.19,1386.66 1894.14,1387.56 \n",
       "  1895.1,1388.77 1896.05,1388.4 1897.01,1388.03 1897.96,1388.02 1898.92,1387.98 1899.87,1387.62 1900.83,1388.16 1901.79,1388.14 1902.74,1388.91 1903.7,1388.75 \n",
       "  1904.65,1388.42 1905.61,1388.96 1906.56,1388.09 1907.52,1387.88 1908.47,1388.05 1909.43,1389.01 1910.38,1388.96 1911.34,1387.76 1912.3,1387.46 1913.25,1387.19 \n",
       "  1914.21,1387.16 1915.16,1387.59 1916.12,1386.96 1917.07,1387.05 1918.03,1387.44 1918.98,1387.64 1919.94,1386.99 1920.9,1386.92 1921.85,1386.71 1922.81,1386.87 \n",
       "  1923.76,1385.92 1924.72,1385.31 1925.67,1385.49 1926.63,1383.87 1927.58,1383.95 1928.54,1385.15 1929.49,1385.12 1930.45,1384.19 1931.41,1383.26 1932.36,1382.51 \n",
       "  1933.32,1382.7 1934.27,1382.7 1935.23,1381.75 1936.18,1382.16 1937.14,1381.62 1938.09,1381.85 1939.05,1381.65 1940.01,1382.03 1940.96,1381.43 1941.92,1382.77 \n",
       "  1942.87,1382.3 1943.83,1382.71 1944.78,1383.94 1945.74,1384.83 1946.69,1384.15 1947.65,1383.82 1948.61,1385.38 1949.56,1385.49 1950.52,1383.6 1951.47,1383.64 \n",
       "  1952.43,1384.1 1953.38,1383.64 1954.34,1384.25 1955.29,1384.14 1956.25,1383.6 1957.2,1383.32 1958.16,1383.05 1959.12,1383.17 1960.07,1382.04 1961.03,1380.73 \n",
       "  1961.98,1381.11 1962.94,1380.18 1963.89,1380.47 1964.85,1380.17 1965.8,1379.61 1966.76,1380.3 1967.72,1380.64 1968.67,1379.73 1969.63,1379.83 1970.58,1379.8 \n",
       "  1971.54,1379.31 1972.49,1377.87 1973.45,1378.83 1974.4,1377.35 1975.36,1378.44 1976.31,1378.97 1977.27,1378.07 1978.23,1378.2 1979.18,1378.48 1980.14,1377.89 \n",
       "  1981.09,1377.95 1982.05,1377.79 1983,1376.75 1983.96,1376.06 1984.91,1375.51 1985.87,1375.01 1986.83,1374.68 1987.78,1373.5 1988.74,1372.34 1989.69,1372.21 \n",
       "  1990.65,1371.27 1991.6,1370.92 1992.56,1370.76 1993.51,1370.69 1994.47,1371.5 1995.42,1371.18 1996.38,1370.34 1997.34,1370.8 1998.29,1370.4 1999.25,1369.55 \n",
       "  2000.2,1369.48 2001.16,1369.33 2002.11,1368.95 2003.07,1368.04 2004.02,1367.48 2004.98,1366.64 2005.94,1366.8 2006.89,1366.78 2007.85,1367.04 2008.8,1366.87 \n",
       "  2009.76,1366.78 2010.71,1367.2 2011.67,1367.59 2012.62,1367.38 2013.58,1367.24 2014.54,1367.33 2015.49,1366.84 2016.45,1366.18 2017.4,1365.64 2018.36,1366.33 \n",
       "  2019.31,1366.11 2020.27,1365.96 2021.22,1365.34 2022.18,1364.99 2023.13,1364.75 2024.09,1365.08 2025.05,1364.85 2026,1363.87 2026.96,1362.6 2027.91,1362.92 \n",
       "  2028.87,1362.3 2029.82,1363.04 2030.78,1361.72 2031.73,1361.13 2032.69,1362.21 2033.65,1362.43 2034.6,1362.59 2035.56,1358.5 2036.51,1358.82 2037.47,1358.31 \n",
       "  2038.42,1358.54 2039.38,1356.84 2040.33,1355.97 2041.29,1354.02 2042.24,1353.41 2043.2,1353.19 2044.16,1352.08 2045.11,1352.84 2046.07,1353.74 2047.02,1352.58 \n",
       "  2047.98,1351.37 2048.93,1350.61 2049.89,1351.17 2050.84,1351.4 2051.8,1350.62 2052.76,1351.12 2053.71,1351.36 2054.67,1351.1 2055.62,1350.47 2056.58,1350.37 \n",
       "  2057.53,1350.56 2058.49,1350.3 2059.44,1350.11 2060.4,1350.21 2061.35,1349.06 2062.31,1351.21 2063.27,1351.69 2064.22,1352.72 2065.18,1352.63 2066.13,1352.74 \n",
       "  2067.09,1352.57 2068.04,1353 2069,1352.55 2069.95,1353.91 2070.91,1353.58 2071.87,1354.42 2072.82,1354.26 2073.78,1354.14 2074.73,1355.29 2075.69,1356.17 \n",
       "  2076.64,1355.92 2077.6,1354.86 2078.55,1354.45 2079.51,1354.21 2080.47,1354.87 2081.42,1354.49 2082.38,1354.73 2083.33,1354.97 2084.29,1354.92 2085.24,1354.36 \n",
       "  2086.2,1355.62 2087.15,1355.52 2088.11,1354.6 2089.06,1355.85 2090.02,1355.2 2090.98,1354.09 2091.93,1354.35 2092.89,1353.18 2093.84,1352.84 2094.8,1348.85 \n",
       "  2095.75,1348.67 2096.71,1349.19 2097.66,1349 2098.62,1348.79 2099.58,1349.05 2100.53,1347.83 2101.49,1349.25 2102.44,1350.02 2103.4,1349.49 2104.35,1348.73 \n",
       "  2105.31,1347.41 2106.26,1348.45 2107.22,1348.93 2108.17,1347.57 2109.13,1347.36 2110.09,1347.43 2111.04,1346.99 2112,1346.96 2112.95,1344.84 2113.91,1346.88 \n",
       "  2114.86,1347.92 2115.82,1346.99 2116.77,1348.29 2117.73,1346.84 2118.69,1349.83 2119.64,1349.86 2120.6,1350.6 2121.55,1349.26 2122.51,1347.42 2123.46,1347.76 \n",
       "  2124.42,1348.02 2125.37,1347.17 2126.33,1346.35 2127.28,1346.16 2128.24,1344.81 2129.2,1345.1 2130.15,1345.66 2131.11,1346.41 2132.06,1345.85 2133.02,1345.99 \n",
       "  2133.97,1345.87 2134.93,1345.61 2135.88,1344.51 2136.84,1343.68 2137.8,1343.08 2138.75,1342.49 2139.71,1342.22 2140.66,1342.3 2141.62,1341.48 2142.57,1342.93 \n",
       "  2143.53,1344.02 2144.48,1343.17 2145.44,1343.57 2146.4,1344.46 2147.35,1343.79 2148.31,1344.74 2149.26,1344.88 2150.22,1345.37 2151.17,1344.89 2152.13,1343.92 \n",
       "  2153.08,1343.51 2154.04,1344.96 2154.99,1342.16 2155.95,1341.03 2156.91,1342.1 2157.86,1342.04 2158.82,1341.2 2159.77,1339.71 2160.73,1339.86 2161.68,1340.23 \n",
       "  2162.64,1339.99 2163.59,1340.8 2164.55,1339.98 2165.51,1339.3 2166.46,1339.55 2167.42,1340.23 2168.37,1340.91 2169.33,1341.74 2170.28,1341.79 2171.24,1339.81 \n",
       "  2172.19,1339.81 2173.15,1339.98 2174.1,1340.83 2175.06,1340.91 2176.02,1339.65 2176.97,1340.47 2177.93,1340.89 2178.88,1339.93 2179.84,1338.67 2180.79,1338.38 \n",
       "  2181.75,1338.85 2182.7,1338.96 2183.66,1338.36 2184.62,1338.71 2185.57,1334.62 2186.53,1334.53 2187.48,1334.31 2188.44,1333.33 2189.39,1332.54 2190.35,1332.01 \n",
       "  2191.3,1332.85 2192.26,1332.56 2193.21,1333.21 2194.17,1333.65 2195.13,1333.53 2196.08,1333.69 2197.04,1334.09 2197.99,1334.2 2198.95,1332.64 2199.9,1333.18 \n",
       "  2200.86,1333.51 2201.81,1333.75 2202.77,1334.3 2203.73,1332.87 2204.68,1333.41 2205.64,1333.29 2206.59,1333.37 2207.55,1333.76 2208.5,1335.87 2209.46,1333.91 \n",
       "  2210.41,1335.8 2211.37,1333.72 2212.33,1335.66 2213.28,1333.62 2214.24,1336 2215.19,1336.82 2216.15,1335.85 2217.1,1335.11 2218.06,1334.54 2219.01,1333.52 \n",
       "  2219.97,1335.36 2220.92,1336.68 2221.88,1335.12 2222.84,1331.39 2223.79,1330.8 2224.75,1333.65 2225.7,1332.27 2226.66,1332.51 2227.61,1331.96 2228.57,1331.82 \n",
       "  2229.52,1331.39 2230.48,1331.36 2231.44,1331.07 2232.39,1329.96 2233.35,1330.7 2234.3,1332.7 2235.26,1332.91 2236.21,1331.67 2237.17,1330.67 2238.12,1330.93 \n",
       "  2239.08,1329.42 2240.03,1327.88 2240.99,1328.37 2241.95,1328.16 2242.9,1328.59 2243.86,1328.59 2244.81,1328.53 2245.77,1327.21 2246.72,1327.38 2247.68,1328.55 \n",
       "  2248.63,1329.15 2249.59,1329.51 2250.55,1329.24 2251.5,1329.18 2252.46,1331.37 2253.41,1330.98 2254.37,1329.64 2255.32,1330.28 2256.28,1330.09 2257.23,1329.21 \n",
       "  2258.19,1327.8 2259.14,1328.08 2260.1,1328.59 2261.06,1330.01 2262.01,1330.07 2262.97,1328.27 2263.92,1329.19 2264.88,1330.62 2265.83,1329.83 2266.79,1330.11 \n",
       "  2267.74,1330.16 2268.7,1330.49 2269.66,1330.12 2270.61,1329.63 2271.57,1328.65 2272.52,1326.44 2273.48,1326.75 2274.43,1327.28 2275.39,1328.17 2276.34,1329.05 \n",
       "  2277.3,1328.69 2278.26,1328.78 2279.21,1328.58 2280.17,1330.12 2281.12,1330.92 2282.08,1330.36 2283.03,1329.87 2283.99,1328.58 2284.94,1328.91 2285.9,1330.08 \n",
       "  2286.85,1328.07 2287.81,1326.51 2288.77,1327.56 2289.72,1327.21 2290.68,1326.78 2291.63,1327.5 2292.59,1327.92 2293.54,1328.66 2294.5,1328.21 2295.45,1327.64 \n",
       "  \n",
       "  \"/>\n",
       "<polyline clip-path=\"url(#clip6002)\" style=\"stroke:#e26f46; stroke-width:4; stroke-opacity:1; fill:none\" points=\"\n",
       "  385.396,1445.28 386.351,1445.27 387.307,1445.15 388.262,1443.9 389.218,1444.34 390.173,1442.83 391.129,1442.58 392.084,1442.9 393.04,1441.67 393.995,1443.7 \n",
       "  394.951,1442.6 395.906,1442.81 396.862,1442.85 397.817,1441.35 398.773,1441.28 399.728,1441.71 400.684,1441.65 401.639,1438.28 402.595,1436.98 403.55,1436.53 \n",
       "  404.506,1438.21 405.461,1435.02 406.417,1433.8 407.372,1434.18 408.328,1433.15 409.283,1431.63 410.239,1429.21 411.194,1431.06 412.15,1431.41 413.105,1429.69 \n",
       "  414.061,1429.6 415.016,1428.93 415.972,1428.93 416.927,1426.61 417.883,1425.77 418.838,1425.73 419.794,1425.55 420.749,1425.53 421.705,1425.24 422.66,1424.17 \n",
       "  423.616,1424.81 424.571,1424.69 425.527,1423.48 426.482,1422.01 427.438,1420.76 428.393,1420.3 429.349,1422.8 430.304,1423.04 431.26,1423.91 432.215,1424.82 \n",
       "  433.171,1424.4 434.126,1422.95 435.082,1422.1 436.037,1423.44 436.993,1424.11 437.948,1424.48 438.904,1426.69 439.86,1426.96 440.815,1425.03 441.771,1424.35 \n",
       "  442.726,1422.51 443.682,1422.93 444.637,1422.54 445.593,1421.67 446.548,1422.02 447.504,1421.36 448.459,1421.11 449.415,1421.82 450.37,1422.99 451.326,1422.6 \n",
       "  452.281,1422.25 453.237,1421.5 454.192,1421.33 455.148,1421.7 456.103,1421.42 457.059,1421.52 458.014,1424.36 458.97,1425.42 459.925,1425.23 460.881,1424.5 \n",
       "  461.836,1424.54 462.792,1424.37 463.747,1425.07 464.703,1425.35 465.658,1424.1 466.614,1426.76 467.569,1430.34 468.525,1430.21 469.48,1431.34 470.436,1431.6 \n",
       "  471.391,1430.9 472.347,1430.09 473.302,1431.51 474.258,1430.22 475.213,1430.67 476.169,1430.44 477.124,1429.49 478.08,1428.33 479.035,1427.04 479.991,1428.17 \n",
       "  480.946,1427.04 481.902,1426.83 482.857,1425.72 483.813,1425.29 484.768,1424.93 485.724,1426.73 486.679,1426.57 487.635,1425.28 488.59,1424.55 489.546,1423.86 \n",
       "  490.501,1423.52 491.457,1423.95 492.412,1423.55 493.368,1423.17 494.323,1423.8 495.279,1424.1 496.234,1423.92 497.19,1424.21 498.145,1423.57 499.101,1421.7 \n",
       "  500.056,1420.69 501.012,1421.21 501.967,1420.27 502.923,1419 503.878,1417.72 504.834,1418.21 505.789,1417.77 506.745,1419.92 507.701,1419.77 508.656,1419.91 \n",
       "  509.612,1419.16 510.567,1417.55 511.523,1417.54 512.478,1416.67 513.434,1416.31 514.389,1417.03 515.345,1417.5 516.3,1416.11 517.256,1417.5 518.211,1418.05 \n",
       "  519.167,1416.22 520.122,1415.67 521.078,1415.47 522.033,1417.04 522.989,1416.95 523.944,1416.99 524.9,1416.46 525.855,1417.14 526.811,1418.8 527.766,1417.36 \n",
       "  528.722,1415.54 529.677,1413.19 530.633,1412.14 531.588,1412.85 532.544,1411.3 533.499,1412.25 534.455,1411.32 535.41,1410.61 536.366,1407.76 537.321,1408.85 \n",
       "  538.277,1408.27 539.232,1408.15 540.188,1408.49 541.143,1410.34 542.099,1410.87 543.054,1409.82 544.01,1410.13 544.965,1409.07 545.921,1406.13 546.876,1405.55 \n",
       "  547.832,1406.92 548.787,1409.62 549.743,1410.51 550.698,1407.75 551.654,1406.74 552.609,1406.27 553.565,1405.45 554.52,1406.64 555.476,1406.57 556.431,1405.24 \n",
       "  557.387,1404.39 558.342,1403.87 559.298,1402.11 560.253,1402.37 561.209,1402.2 562.164,1401.9 563.12,1401.92 564.075,1400.97 565.031,1398.84 565.986,1399.49 \n",
       "  566.942,1399.24 567.897,1398.59 568.853,1397.74 569.808,1397.46 570.764,1397.23 571.719,1397.49 572.675,1396.47 573.63,1394.83 574.586,1391.97 575.542,1391.98 \n",
       "  576.497,1393.21 577.453,1391.88 578.408,1395.72 579.364,1395.7 580.319,1394.98 581.275,1393.2 582.23,1393.36 583.186,1393.84 584.141,1394 585.097,1393.04 \n",
       "  586.052,1392.58 587.008,1392.22 587.963,1394.03 588.919,1394.88 589.874,1394 590.83,1391.72 591.785,1391.66 592.741,1391.81 593.696,1392.33 594.652,1393.9 \n",
       "  595.607,1392.73 596.563,1393.67 597.518,1395.07 598.474,1392.01 599.429,1389.29 600.385,1388.75 601.34,1388.5 602.296,1387.08 603.251,1386.91 604.207,1384.67 \n",
       "  605.162,1382.31 606.118,1386.45 607.073,1387.44 608.029,1388 608.984,1385.69 609.94,1384.2 610.895,1384.8 611.851,1383.55 612.806,1383.36 613.762,1383.63 \n",
       "  614.717,1385.63 615.673,1380.92 616.628,1381.42 617.584,1382.6 618.539,1381.32 619.495,1382.51 620.45,1382.48 621.406,1380.2 622.361,1380.49 623.317,1381.41 \n",
       "  624.272,1381.97 625.228,1382.51 626.183,1382.1 627.139,1381.64 628.094,1382.44 629.05,1382.76 630.005,1384.35 630.961,1385.43 631.916,1387.2 632.872,1388.28 \n",
       "  633.827,1387.19 634.783,1383.41 635.738,1383.79 636.694,1389.53 637.649,1390.22 638.605,1391.02 639.56,1390.94 640.516,1390.55 641.471,1392.94 642.427,1392.27 \n",
       "  643.383,1392.28 644.338,1391.96 645.294,1392.15 646.249,1393.63 647.205,1392.82 648.16,1394.24 649.116,1396.29 650.071,1396.15 651.027,1396.74 651.982,1395.81 \n",
       "  652.938,1396.1 653.893,1395.89 654.849,1395.77 655.804,1396.03 656.76,1396.96 657.715,1397.96 658.671,1396.82 659.626,1393.99 660.582,1392.26 661.537,1393.45 \n",
       "  662.493,1392.87 663.448,1395.07 664.404,1395.61 665.359,1396.33 666.315,1395.57 667.27,1395.76 668.226,1396.99 669.181,1397.75 670.137,1396.87 671.092,1396.81 \n",
       "  672.048,1395.07 673.003,1396.3 673.959,1396.71 674.914,1398.38 675.87,1399.72 676.825,1400.64 677.781,1401.04 678.736,1400.13 679.692,1399.3 680.647,1398.85 \n",
       "  681.603,1397.6 682.558,1397.71 683.514,1398.87 684.469,1397.02 685.425,1396.11 686.38,1396.38 687.336,1398.18 688.291,1399.3 689.247,1400.69 690.202,1401.06 \n",
       "  691.158,1403.76 692.113,1403.55 693.069,1404.92 694.024,1404.03 694.98,1404.09 695.935,1405.5 696.891,1404.02 697.846,1407.27 698.802,1404.19 699.757,1403.91 \n",
       "  700.713,1403.19 701.668,1402.97 702.624,1402.71 703.579,1402.37 704.535,1401.91 705.49,1400.84 706.446,1401.77 707.401,1401.12 708.357,1400.83 709.312,1402.35 \n",
       "  710.268,1402.4 711.224,1403.81 712.179,1404.47 713.135,1403.86 714.09,1401.92 715.046,1398.8 716.001,1397.76 716.957,1398.18 717.912,1399.58 718.868,1400.89 \n",
       "  719.823,1400.18 720.779,1400.33 721.734,1400.16 722.69,1399.01 723.645,1398.85 724.601,1397.22 725.556,1396.93 726.512,1396.75 727.467,1396.81 728.423,1397.87 \n",
       "  729.378,1398.06 730.334,1396.62 731.289,1395.45 732.245,1395.8 733.2,1395.93 734.156,1396.25 735.111,1395.99 736.067,1396.18 737.022,1397.31 737.978,1397.86 \n",
       "  738.933,1398.16 739.889,1397.93 740.844,1399.92 741.8,1398.2 742.755,1399.63 743.711,1398.96 744.666,1398.34 745.622,1397.3 746.577,1398.33 747.533,1399.67 \n",
       "  748.488,1398.47 749.444,1398.7 750.399,1398.69 751.355,1399.28 752.31,1397.95 753.266,1397.36 754.221,1397.37 755.177,1398.56 756.132,1396.19 757.088,1394.21 \n",
       "  758.043,1391.13 758.999,1391.3 759.954,1392.31 760.91,1391.37 761.865,1390.1 762.821,1391.33 763.776,1393.58 764.732,1392.39 765.687,1391.62 766.643,1393.04 \n",
       "  767.598,1393.65 768.554,1393.67 769.509,1394.12 770.465,1392.56 771.42,1390.57 772.376,1389.77 773.331,1388.77 774.287,1391.09 775.242,1391.16 776.198,1390.13 \n",
       "  777.153,1389.24 778.109,1390.25 779.065,1390.08 780.02,1390.92 780.976,1390.36 781.931,1390.79 782.887,1391.65 783.842,1392.74 784.798,1392.08 785.753,1392.22 \n",
       "  786.709,1393.74 787.664,1393.45 788.62,1394.71 789.575,1393.31 790.531,1391.37 791.486,1389.04 792.442,1389.53 793.397,1390.41 794.353,1390.28 795.308,1390.71 \n",
       "  796.264,1387.68 797.219,1390.12 798.175,1390.48 799.13,1387.61 800.086,1385.82 801.041,1385.24 801.997,1384.27 802.952,1385.08 803.908,1384.63 804.863,1382.98 \n",
       "  805.819,1381.42 806.774,1379.59 807.73,1380.62 808.685,1379.03 809.641,1379.13 810.596,1378.95 811.552,1378.56 812.507,1381.43 813.463,1380.92 814.418,1379.37 \n",
       "  815.374,1379.43 816.329,1381.25 817.285,1378.11 818.24,1377.26 819.196,1375.08 820.151,1372.4 821.107,1373.03 822.062,1373.63 823.018,1377.62 823.973,1377.85 \n",
       "  824.929,1377.04 825.884,1376.04 826.84,1374.7 827.795,1371.28 828.751,1370.41 829.706,1371.64 830.662,1374.08 831.617,1373.79 832.573,1370.2 833.528,1371.13 \n",
       "  834.484,1371.75 835.439,1372.94 836.395,1371.69 837.35,1369.83 838.306,1368.53 839.261,1369.36 840.217,1370.84 841.172,1370.27 842.128,1370.01 843.083,1371.98 \n",
       "  844.039,1372.83 844.994,1374.59 845.95,1375.32 846.906,1373.51 847.861,1372.44 848.817,1372.14 849.772,1372.63 850.728,1374.58 851.683,1374.34 852.639,1373.41 \n",
       "  853.594,1372.25 854.55,1369.82 855.505,1371.15 856.461,1372.68 857.416,1374.68 858.372,1373.34 859.327,1374.22 860.283,1373.53 861.238,1373.35 862.194,1372.66 \n",
       "  863.149,1372.46 864.105,1372.38 865.06,1373.37 866.016,1374.17 866.971,1373.44 867.927,1374.13 868.882,1372.61 869.838,1371.73 870.793,1370.22 871.749,1368.47 \n",
       "  872.704,1368.38 873.66,1366.82 874.615,1367.71 875.571,1363.57 876.526,1361.86 877.482,1363.28 878.437,1362.36 879.393,1358.77 880.348,1358.36 881.304,1356.99 \n",
       "  882.259,1354.63 883.215,1356.58 884.17,1356.41 885.126,1355.3 886.081,1349.42 887.037,1349.11 887.992,1346.4 888.948,1347.76 889.903,1348.03 890.859,1350.69 \n",
       "  891.814,1350.11 892.77,1350.8 893.725,1349.35 894.681,1348.47 895.636,1345.1 896.592,1344.49 897.547,1345.85 898.503,1341.6 899.458,1343.33 900.414,1343.99 \n",
       "  901.369,1341.31 902.325,1346.03 903.28,1345.62 904.236,1344.35 905.191,1343.98 906.147,1343.52 907.102,1345.94 908.058,1344.15 909.013,1343.79 909.969,1344.31 \n",
       "  910.924,1344.31 911.88,1342.02 912.835,1342.29 913.791,1341.99 914.747,1341.12 915.702,1341.98 916.658,1344.08 917.613,1343.3 918.569,1344.41 919.524,1344.01 \n",
       "  920.48,1345.4 921.435,1345.53 922.391,1343.33 923.346,1344.9 924.302,1343.33 925.257,1341.43 926.213,1340.55 927.168,1342.35 928.124,1341.47 929.079,1341.64 \n",
       "  930.035,1344.54 930.99,1346.86 931.946,1346.6 932.901,1346.67 933.857,1347.74 934.812,1346.2 935.768,1345.31 936.723,1344.63 937.679,1346.81 938.634,1346.05 \n",
       "  939.59,1348.6 940.545,1351.98 941.501,1352.51 942.456,1351.52 943.412,1351.48 944.367,1351.81 945.323,1351.8 946.278,1350.43 947.234,1347.67 948.189,1348.42 \n",
       "  949.145,1348.14 950.1,1346.7 951.056,1350.15 952.011,1352 952.967,1352.71 953.922,1351.49 954.878,1352.59 955.833,1355.26 956.789,1354.12 957.744,1355.3 \n",
       "  958.7,1355.84 959.655,1355.67 960.611,1354.27 961.566,1351.77 962.522,1353.54 963.477,1351.66 964.433,1349.07 965.388,1350.8 966.344,1352.65 967.299,1353.18 \n",
       "  968.255,1350.95 969.21,1350.75 970.166,1351.8 971.121,1352.47 972.077,1351.31 973.032,1350.08 973.988,1347.22 974.943,1347.49 975.899,1348.9 976.854,1347.7 \n",
       "  977.81,1346.89 978.765,1347.66 979.721,1347.68 980.676,1347.4 981.632,1349.96 982.587,1355.2 983.543,1352.32 984.499,1350.78 985.454,1352.66 986.41,1353.93 \n",
       "  987.365,1355.37 988.321,1354.2 989.276,1352.5 990.232,1350.51 991.187,1351.21 992.143,1352.29 993.098,1355.04 994.054,1353.46 995.009,1355.06 995.965,1355.24 \n",
       "  996.92,1352.6 997.876,1356.78 998.831,1355.82 999.787,1353.58 1000.74,1355.14 1001.7,1357.09 1002.65,1356.38 1003.61,1355.33 1004.56,1357.17 1005.52,1356.38 \n",
       "  1006.48,1358.74 1007.43,1357.11 1008.39,1358.49 1009.34,1359.74 1010.3,1368.99 1011.25,1367.56 1012.21,1368.06 1013.16,1368.32 1014.12,1366.95 1015.07,1365.49 \n",
       "  1016.03,1365.34 1016.99,1365.54 1017.94,1367.7 1018.9,1368.47 1019.85,1370.21 1020.81,1370.6 1021.76,1371.79 1022.72,1372.09 1023.67,1371.28 1024.63,1372.05 \n",
       "  1025.59,1371.89 1026.54,1371.33 1027.5,1368.36 1028.45,1369.5 1029.41,1371.33 1030.36,1371.1 1031.32,1369.52 1032.27,1367.41 1033.23,1368.01 1034.18,1368.02 \n",
       "  1035.14,1367.28 1036.1,1369.14 1037.05,1367.02 1038.01,1364.49 1038.96,1365.18 1039.92,1362.14 1040.87,1359.65 1041.83,1360.56 1042.78,1363.21 1043.74,1365.14 \n",
       "  1044.7,1365.19 1045.65,1367.43 1046.61,1367.16 1047.56,1365.05 1048.52,1362.94 1049.47,1364.52 1050.43,1364.41 1051.38,1364.46 1052.34,1364.05 1053.3,1359.47 \n",
       "  1054.25,1359.36 1055.21,1358.09 1056.16,1359.77 1057.12,1361.41 1058.07,1359.76 1059.03,1362.75 1059.98,1360.08 1060.94,1361.21 1061.89,1357.95 1062.85,1354.56 \n",
       "  1063.81,1355.73 1064.76,1356.92 1065.72,1358.23 1066.67,1359.78 1067.63,1356.99 1068.58,1358.17 1069.54,1359.37 1070.49,1358.96 1071.45,1358.9 1072.41,1364.85 \n",
       "  1073.36,1363.33 1074.32,1362.66 1075.27,1361.55 1076.23,1360.74 1077.18,1360.61 1078.14,1361.46 1079.09,1361.81 1080.05,1360.05 1081,1360.43 1081.96,1360.41 \n",
       "  1082.92,1360.38 1083.87,1364.2 1084.83,1363.11 1085.78,1362.75 1086.74,1362.11 1087.69,1359.35 1088.65,1354 1089.6,1351.9 1090.56,1352.34 1091.52,1351.19 \n",
       "  1092.47,1351.84 1093.43,1353.73 1094.38,1355.6 1095.34,1352.03 1096.29,1353.97 1097.25,1353.82 1098.2,1354.85 1099.16,1352.57 1100.11,1352.51 1101.07,1352.75 \n",
       "  1102.03,1352.96 1102.98,1352.7 1103.94,1353.31 1104.89,1353.36 1105.85,1355.58 1106.8,1355.16 1107.76,1356.83 1108.71,1357.03 1109.67,1355.46 1110.63,1356.21 \n",
       "  1111.58,1354.56 1112.54,1355.64 1113.49,1354.38 1114.45,1349.66 1115.4,1349.24 1116.36,1350.68 1117.31,1352.41 1118.27,1352.04 1119.23,1351.91 1120.18,1352.74 \n",
       "  1121.14,1353.99 1122.09,1352.93 1123.05,1349.72 1124,1347.8 1124.96,1347.55 1125.91,1348.97 1126.87,1350.17 1127.82,1349.36 1128.78,1349.26 1129.74,1348.78 \n",
       "  1130.69,1348.25 1131.65,1348.29 1132.6,1346.96 1133.56,1344.79 1134.51,1342.92 1135.47,1340.73 1136.42,1340.1 1137.38,1340.6 1138.34,1338.72 1139.29,1338.29 \n",
       "  1140.25,1339.84 1141.2,1344.4 1142.16,1342.18 1143.11,1341.6 1144.07,1343.06 1145.02,1345.86 1145.98,1343.36 1146.93,1342.59 1147.89,1342.51 1148.85,1341.45 \n",
       "  1149.8,1343.56 1150.76,1341.65 1151.71,1342.23 1152.67,1340.05 1153.62,1337.75 1154.58,1338.27 1155.53,1336.72 1156.49,1335.66 1157.45,1336.18 1158.4,1336.46 \n",
       "  1159.36,1336.17 1160.31,1337.13 1161.27,1338.44 1162.22,1338.38 1163.18,1336.62 1164.13,1334.92 1165.09,1334.91 1166.04,1335.66 1167,1335.34 1167.96,1337.59 \n",
       "  1168.91,1338.04 1169.87,1339.28 1170.82,1338.72 1171.78,1341.04 1172.73,1338.53 1173.69,1338.8 1174.64,1340.83 1175.6,1340.5 1176.56,1340.12 1177.51,1339.16 \n",
       "  1178.47,1337.9 1179.42,1337.58 1180.38,1337.7 1181.33,1340.74 1182.29,1343.05 1183.24,1345.32 1184.2,1345.33 1185.15,1344.19 1186.11,1344.71 1187.07,1344.22 \n",
       "  1188.02,1345.75 1188.98,1342.32 1189.93,1343.52 1190.89,1343.39 1191.84,1343.99 1192.8,1345.53 1193.75,1344.58 1194.71,1344.81 1195.67,1343.61 1196.62,1341.89 \n",
       "  1197.58,1342.43 1198.53,1342.47 1199.49,1341.87 1200.44,1342.22 1201.4,1341.44 1202.35,1341 1203.31,1340.7 1204.27,1341.75 1205.22,1341.85 1206.18,1342.69 \n",
       "  1207.13,1342.22 1208.09,1344.92 1209.04,1347.17 1210,1346.52 1210.95,1347.81 1211.91,1348.38 1212.86,1350.18 1213.82,1352.62 1214.78,1352.77 1215.73,1351.69 \n",
       "  1216.69,1352.65 1217.64,1353.22 1218.6,1353.52 1219.55,1352.9 1220.51,1352.67 1221.46,1346.09 1222.42,1347.22 1223.38,1346.72 1224.33,1346.07 1225.29,1345.76 \n",
       "  1226.24,1346.38 1227.2,1344.67 1228.15,1345.22 1229.11,1348.39 1230.06,1348.11 1231.02,1349.42 1231.97,1348.3 1232.93,1349.5 1233.89,1349.63 1234.84,1345.8 \n",
       "  1235.8,1345.76 1236.75,1345.76 1237.71,1345.6 1238.66,1345.69 1239.62,1346.46 1240.57,1349.92 1241.53,1352.02 1242.49,1349.79 1243.44,1350 1244.4,1349.03 \n",
       "  1245.35,1349 1246.31,1350.81 1247.26,1344.97 1248.22,1344.69 1249.17,1348.27 1250.13,1352.91 1251.08,1351.23 1252.04,1350.96 1253,1355.59 1253.95,1360.58 \n",
       "  1254.91,1358.7 1255.86,1359.84 1256.82,1360.9 1257.77,1359.38 1258.73,1358.74 1259.68,1358.76 1260.64,1359.08 1261.6,1359.65 1262.55,1361.93 1263.51,1358.84 \n",
       "  1264.46,1360.06 1265.42,1359.6 1266.37,1358.8 1267.33,1363.08 1268.28,1362.04 1269.24,1364.33 1270.2,1363.64 1271.15,1361.18 1272.11,1359.97 1273.06,1355.04 \n",
       "  1274.02,1353.84 1274.97,1356.64 1275.93,1351.35 1276.88,1351.11 1277.84,1352.02 1278.79,1353.44 1279.75,1352.57 1280.71,1352.82 1281.66,1351.23 1282.62,1352.56 \n",
       "  1283.57,1353.06 1284.53,1351.73 1285.48,1351.91 1286.44,1350.56 1287.39,1349.14 1288.35,1346.58 1289.31,1346.79 1290.26,1344.65 1291.22,1341.51 1292.17,1342.14 \n",
       "  1293.13,1339 1294.08,1340.5 1295.04,1339.46 1295.99,1341.02 1296.95,1341.38 1297.9,1338.11 1298.86,1336.11 1299.82,1334.41 1300.77,1337 1301.73,1336.69 \n",
       "  1302.68,1337.64 1303.64,1336.23 1304.59,1338.44 1305.55,1337.36 1306.5,1341.78 1307.46,1343.4 1308.42,1346.57 1309.37,1347 1310.33,1347.5 1311.28,1341.63 \n",
       "  1312.24,1341.68 1313.19,1343.56 1314.15,1340.75 1315.1,1339.92 1316.06,1336.63 1317.01,1339.44 1317.97,1339.84 1318.93,1340.41 1319.88,1339.63 1320.84,1339.09 \n",
       "  1321.79,1342.14 1322.75,1339.22 1323.7,1336.86 1324.66,1337.8 1325.61,1336.46 1326.57,1335.02 1327.53,1335.06 1328.48,1336.16 1329.44,1337.79 1330.39,1337.23 \n",
       "  1331.35,1337.88 1332.3,1340.87 1333.26,1340.47 1334.21,1343.15 1335.17,1342.62 1336.13,1345.34 1337.08,1345.5 1338.04,1346.85 1338.99,1343.1 1339.95,1341.64 \n",
       "  1340.9,1340.27 1341.86,1341.01 1342.81,1342.64 1343.77,1342.71 1344.72,1341.74 1345.68,1343.08 1346.64,1344.69 1347.59,1344.96 1348.55,1344.25 1349.5,1339.75 \n",
       "  1350.46,1338.67 1351.41,1332.5 1352.37,1337.86 1353.32,1341.03 1354.28,1347.08 1355.24,1337.5 1356.19,1337.05 1357.15,1337.36 1358.1,1337.03 1359.06,1339.71 \n",
       "  1360.01,1338.48 1360.97,1340.99 1361.92,1338.87 1362.88,1339.53 1363.83,1340.37 1364.79,1337.44 1365.75,1336.53 1366.7,1336.59 1367.66,1339.33 1368.61,1340.96 \n",
       "  1369.57,1338.05 1370.52,1338.96 1371.48,1338.37 1372.43,1338.18 1373.39,1336.86 1374.35,1338.29 1375.3,1336.14 1376.26,1341.9 1377.21,1339.71 1378.17,1341.46 \n",
       "  1379.12,1337.54 1380.08,1337 1381.03,1335.96 1381.99,1338.32 1382.94,1339.29 1383.9,1343.09 1384.86,1343.98 1385.81,1342.98 1386.77,1342.92 1387.72,1345.68 \n",
       "  1388.68,1350.17 1389.63,1353.25 1390.59,1353.68 1391.54,1351.39 1392.5,1349.88 1393.46,1351.78 1394.41,1354.88 1395.37,1351.24 1396.32,1352.3 1397.28,1344.35 \n",
       "  1398.23,1339.03 1399.19,1337.2 1400.14,1337.34 1401.1,1335.58 1402.06,1336.67 1403.01,1332.77 1403.97,1330.16 1404.92,1332.55 1405.88,1328.41 1406.83,1329.21 \n",
       "  1407.79,1330.34 1408.74,1328.08 1409.7,1330.45 1410.65,1330.28 1411.61,1330.48 1412.57,1330.22 1413.52,1329.3 1414.48,1331.59 1415.43,1329.56 1416.39,1329.96 \n",
       "  1417.34,1328.81 1418.3,1330.93 1419.25,1328.59 1420.21,1331.47 1421.17,1326.05 1422.12,1327.36 1423.08,1324.29 1424.03,1325.79 1424.99,1325.84 1425.94,1328.31 \n",
       "  1426.9,1327.6 1427.85,1327.4 1428.81,1329.08 1429.76,1331.87 1430.72,1330.84 1431.68,1329.78 1432.63,1329.13 1433.59,1326.89 1434.54,1328.68 1435.5,1325.26 \n",
       "  1436.45,1324.91 1437.41,1326.17 1438.36,1328.95 1439.32,1327.31 1440.28,1322.59 1441.23,1319.3 1442.19,1315.86 1443.14,1313.55 1444.1,1315.96 1445.05,1318.96 \n",
       "  1446.01,1320.87 1446.96,1317.21 1447.92,1311.21 1448.87,1315.52 1449.83,1314.75 1450.79,1313.72 1451.74,1315.37 1452.7,1316.23 1453.65,1312.71 1454.61,1314.42 \n",
       "  1455.56,1315.97 1456.52,1314.14 1457.47,1311.33 1458.43,1313.41 1459.39,1314.41 1460.34,1315.23 1461.3,1312.82 1462.25,1321.03 1463.21,1317.99 1464.16,1318.85 \n",
       "  1465.12,1316.04 1466.07,1312.3 1467.03,1312.36 1467.99,1313.46 1468.94,1309.75 1469.9,1308.56 1470.85,1316.02 1471.81,1314.82 1472.76,1312.38 1473.72,1307.34 \n",
       "  1474.67,1308.57 1475.63,1319.62 1476.58,1322.33 1477.54,1329.74 1478.5,1330.42 1479.45,1335.29 1480.41,1331.71 1481.36,1333.97 1482.32,1335.3 1483.27,1333.83 \n",
       "  1484.23,1333.57 1485.18,1333.42 1486.14,1333.61 1487.1,1334.84 1488.05,1330.18 1489.01,1331.24 1489.96,1335.59 1490.92,1332.49 1491.87,1330.26 1492.83,1330.89 \n",
       "  1493.78,1327.39 1494.74,1326.88 1495.69,1326.62 1496.65,1326.43 1497.61,1327.96 1498.56,1328.89 1499.52,1329.23 1500.47,1328.32 1501.43,1331.25 1502.38,1333.31 \n",
       "  1503.34,1332.71 1504.29,1331.74 1505.25,1332.52 1506.21,1330.47 1507.16,1328.68 1508.12,1329 1509.07,1330.35 1510.03,1333.41 1510.98,1331.26 1511.94,1329.64 \n",
       "  1512.89,1325.42 1513.85,1328.83 1514.8,1323.9 1515.76,1325.22 1516.72,1331.38 1517.67,1325.7 1518.63,1334.45 1519.58,1337.99 1520.54,1340.73 1521.49,1342.17 \n",
       "  1522.45,1334.75 1523.4,1335.82 1524.36,1338.36 1525.32,1338.11 1526.27,1340.09 1527.23,1342.82 1528.18,1343.9 1529.14,1347.27 1530.09,1342.94 1531.05,1344.73 \n",
       "  1532,1349.11 1532.96,1352.58 1533.92,1346.74 1534.87,1350.02 1535.83,1360.29 1536.78,1353.24 1537.74,1349.83 1538.69,1346.05 1539.65,1352.29 1540.6,1358.8 \n",
       "  1541.56,1364.65 1542.51,1367.18 1543.47,1367.46 1544.43,1354.25 1545.38,1350.52 1546.34,1342.02 1547.29,1342.33 1548.25,1344.13 1549.2,1345.94 1550.16,1350.91 \n",
       "  1551.11,1353.57 1552.07,1358.43 1553.03,1362.56 1553.98,1364.02 1554.94,1370.33 1555.89,1363.22 1556.85,1367.99 1557.8,1367.37 1558.76,1370.86 1559.71,1370.81 \n",
       "  1560.67,1370.42 1561.62,1363.01 1562.58,1358.83 1563.54,1355.18 1564.49,1350.37 1565.45,1350.03 1566.4,1357.12 1567.36,1353.89 1568.31,1350.57 1569.27,1345.3 \n",
       "  1570.22,1340.63 1571.18,1339.36 1572.14,1347.06 1573.09,1350.25 1574.05,1352.46 1575,1349.06 1575.96,1351.21 1576.91,1348.41 1577.87,1342.63 1578.82,1337.64 \n",
       "  1579.78,1337.23 1580.73,1342.98 1581.69,1345.72 1582.65,1345.68 1583.6,1343.44 1584.56,1344.83 1585.51,1343.47 1586.47,1340.25 1587.42,1337.28 1588.38,1338 \n",
       "  1589.33,1341.54 1590.29,1342.6 1591.25,1342.01 1592.2,1343.19 1593.16,1339 1594.11,1338.44 1595.07,1342.97 1596.02,1334.5 1596.98,1330.68 1597.93,1327.41 \n",
       "  1598.89,1331.27 1599.85,1322.19 1600.8,1326.84 1601.76,1328.83 1602.71,1333.71 1603.67,1329.65 1604.62,1331.73 1605.58,1330.04 1606.53,1328.18 1607.49,1321.29 \n",
       "  1608.44,1325.83 1609.4,1322.19 1610.36,1326.26 1611.31,1333.59 1612.27,1334.94 1613.22,1339.84 1614.18,1331.81 1615.13,1332.82 1616.09,1333.67 1617.04,1329.68 \n",
       "  1618,1324.9 1618.96,1323.28 1619.91,1329.1 1620.87,1328.99 1621.82,1335.27 1622.78,1339.53 1623.73,1329.21 1624.69,1333.37 1625.64,1333.65 1626.6,1330.44 \n",
       "  1627.55,1331.1 1628.51,1331.57 1629.47,1343.8 1630.42,1344.9 1631.38,1344.33 1632.33,1341.17 1633.29,1336.97 1634.24,1339.89 1635.2,1335.78 1636.15,1339.72 \n",
       "  1637.11,1334.54 1638.07,1333 1639.02,1330.64 1639.98,1334.46 1640.93,1334.83 1641.89,1330.39 1642.84,1331.64 1643.8,1328.93 1644.75,1334.97 1645.71,1334.43 \n",
       "  1646.66,1325.5 1647.62,1324.3 1648.58,1325.84 1649.53,1328.1 1650.49,1322.38 1651.44,1328.6 1652.4,1334.66 1653.35,1339.93 1654.31,1334.34 1655.26,1333.37 \n",
       "  1656.22,1329.52 1657.18,1328.44 1658.13,1330.97 1659.09,1321.52 1660.04,1320.91 1661,1322.52 1661.95,1322.48 1662.91,1317.47 1663.86,1323.38 1664.82,1323.62 \n",
       "  1665.78,1326.62 1666.73,1325.92 1667.69,1327.19 1668.64,1333.23 1669.6,1340.57 1670.55,1338.9 1671.51,1339.43 1672.46,1341.1 1673.42,1342.33 1674.37,1341.91 \n",
       "  1675.33,1340.01 1676.29,1338.63 1677.24,1335.4 1678.2,1335.69 1679.15,1332.7 1680.11,1330.27 1681.06,1325.52 1682.02,1325.29 1682.97,1324.67 1683.93,1317.11 \n",
       "  1684.89,1316.94 1685.84,1320.85 1686.8,1319.44 1687.75,1321.67 1688.71,1322.55 1689.66,1323.03 1690.62,1321.85 1691.57,1326.08 1692.53,1332.3 1693.48,1332.82 \n",
       "  1694.44,1333.71 1695.4,1334.21 1696.35,1332.96 1697.31,1330.39 1698.26,1330.92 1699.22,1330.91 1700.17,1333 1701.13,1334.89 1702.08,1334.11 1703.04,1336.66 \n",
       "  1704,1336.54 1704.95,1340.76 1705.91,1340.86 1706.86,1344.05 1707.82,1338.6 1708.77,1342.41 1709.73,1339.73 1710.68,1338.91 1711.64,1340.2 1712.59,1340.91 \n",
       "  1713.55,1341 1714.51,1340.46 1715.46,1340.35 1716.42,1341.48 1717.37,1337.92 1718.33,1340.18 1719.28,1334.31 1720.24,1340.5 1721.19,1337.27 1722.15,1340.15 \n",
       "  1723.11,1340.4 1724.06,1338.35 1725.02,1335.11 1725.97,1336.52 1726.93,1338.25 1727.88,1337.09 1728.84,1339.5 1729.79,1339.95 1730.75,1334.07 1731.71,1335.09 \n",
       "  1732.66,1335.34 1733.62,1333.58 1734.57,1335.88 1735.53,1338.32 1736.48,1340.52 1737.44,1340.63 1738.39,1337.94 1739.35,1337.54 1740.3,1339.11 1741.26,1339.92 \n",
       "  1742.22,1340.91 1743.17,1338.82 1744.13,1336.1 1745.08,1339.53 1746.04,1341.78 1746.99,1341.59 1747.95,1342.84 1748.9,1338.98 1749.86,1337.5 1750.82,1333.32 \n",
       "  1751.77,1331.95 1752.73,1332.41 1753.68,1331.37 1754.64,1330.6 1755.59,1332.3 1756.55,1330.06 1757.5,1329.6 1758.46,1327.7 1759.41,1327.49 1760.37,1328.62 \n",
       "  1761.33,1329.81 1762.28,1329.36 1763.24,1327.14 1764.19,1327.43 1765.15,1325.23 1766.1,1318.88 1767.06,1322.81 1768.01,1323.18 1768.97,1322.08 1769.93,1321.18 \n",
       "  1770.88,1321.54 1771.84,1324.37 1772.79,1326.5 1773.75,1328.24 1774.7,1328.12 1775.66,1328.64 1776.61,1327.28 1777.57,1324.67 1778.52,1322.3 1779.48,1324.35 \n",
       "  1780.44,1324.76 1781.39,1324.77 1782.35,1330.07 1783.3,1329.07 1784.26,1329.3 1785.21,1326.86 1786.17,1324.03 1787.12,1325.48 1788.08,1323.36 1789.04,1322.01 \n",
       "  1789.99,1323.12 1790.95,1318.5 1791.9,1315.71 1792.86,1314.58 1793.81,1315 1794.77,1315.22 1795.72,1314.28 1796.68,1312.46 1797.63,1309.31 1798.59,1311.95 \n",
       "  1799.55,1314.16 1800.5,1313.15 1801.46,1312.3 1802.41,1310.54 1803.37,1309.86 1804.32,1306.52 1805.28,1307.3 1806.23,1307.56 1807.19,1308.81 1808.15,1307.82 \n",
       "  1809.1,1313.11 1810.06,1315.33 1811.01,1313.33 1811.97,1312.62 1812.92,1314.99 1813.88,1310.5 1814.83,1309.4 1815.79,1308.4 1816.75,1307.31 1817.7,1306.39 \n",
       "  1818.66,1307.57 1819.61,1305.12 1820.57,1306 1821.52,1304.12 1822.48,1303.54 1823.43,1304.15 1824.39,1304.89 1825.34,1304.83 1826.3,1305.04 1827.26,1305.9 \n",
       "  1828.21,1310.21 1829.17,1309.27 1830.12,1311.35 1831.08,1310.79 1832.03,1313.3 1832.99,1314.56 1833.94,1313.3 1834.9,1313.05 1835.86,1317.84 1836.81,1316.69 \n",
       "  1837.77,1316.51 1838.72,1319.07 1839.68,1316.2 1840.63,1315.57 1841.59,1316.56 1842.54,1315.28 1843.5,1317.84 1844.45,1323.77 1845.41,1323.09 1846.37,1321.41 \n",
       "  1847.32,1320.93 1848.28,1321.91 1849.23,1324.65 1850.19,1326.95 1851.14,1326.86 1852.1,1324.19 1853.05,1323.58 1854.01,1322.96 1854.97,1322.38 1855.92,1321.06 \n",
       "  1856.88,1319.99 1857.83,1321.46 1858.79,1322 1859.74,1324.52 1860.7,1324.08 1861.65,1323.93 1862.61,1324.95 1863.56,1324.67 1864.52,1325.2 1865.48,1321.7 \n",
       "  1866.43,1322.4 1867.39,1320.72 1868.34,1321.02 1869.3,1321.91 1870.25,1322.58 1871.21,1321.1 1872.16,1319.82 1873.12,1319.02 1874.08,1317.85 1875.03,1318.11 \n",
       "  1875.99,1318.37 1876.94,1313.34 1877.9,1312.71 1878.85,1311.88 1879.81,1312.75 1880.76,1315.78 1881.72,1314.84 1882.68,1314.52 1883.63,1314.72 1884.59,1316.11 \n",
       "  1885.54,1315.64 1886.5,1313.8 1887.45,1312.45 1888.41,1312.96 1889.36,1313.93 1890.32,1313.4 1891.27,1312.86 1892.23,1313.44 1893.19,1313.56 1894.14,1316.33 \n",
       "  1895.1,1320.05 1896.05,1318.92 1897.01,1317.83 1897.96,1317.8 1898.92,1317.7 1899.87,1316.59 1900.83,1318.26 1901.79,1318.21 1902.74,1320.56 1903.7,1320.08 \n",
       "  1904.65,1319.1 1905.61,1320.74 1906.56,1318.13 1907.52,1317.49 1908.47,1318.03 1909.43,1320.97 1910.38,1320.82 1911.34,1317.2 1912.3,1316.28 1913.25,1315.49 \n",
       "  1914.21,1315.39 1915.16,1316.72 1916.12,1314.81 1917.07,1315.1 1918.03,1316.3 1918.98,1316.92 1919.94,1314.96 1920.9,1314.74 1921.85,1314.11 1922.81,1314.62 \n",
       "  1923.76,1311.73 1924.72,1309.85 1925.67,1310.39 1926.63,1305.42 1927.58,1305.67 1928.54,1309.43 1929.49,1309.36 1930.45,1306.46 1931.41,1303.57 1932.36,1301.23 \n",
       "  1933.32,1301.83 1934.27,1301.84 1935.23,1298.86 1936.18,1300.19 1937.14,1298.47 1938.09,1299.22 1939.05,1298.59 1940.01,1299.82 1940.96,1297.93 1941.92,1302.19 \n",
       "  1942.87,1300.73 1943.83,1302.05 1944.78,1305.92 1945.74,1308.71 1946.69,1306.61 1947.65,1305.61 1948.61,1310.49 1949.56,1310.85 1950.52,1305 1951.47,1305.16 \n",
       "  1952.43,1306.59 1953.38,1305.17 1954.34,1307.07 1955.29,1306.77 1956.25,1305.07 1957.2,1304.21 1958.16,1303.37 1959.12,1303.76 1960.07,1300.24 1961.03,1296.11 \n",
       "  1961.98,1297.33 1962.94,1294.38 1963.89,1295.32 1964.85,1294.37 1965.8,1292.59 1966.76,1294.82 1967.72,1295.9 1968.67,1293.03 1969.63,1293.34 1970.58,1293.28 \n",
       "  1971.54,1291.7 1972.49,1287.09 1973.45,1290.2 1974.4,1285.44 1975.36,1289.01 1976.31,1290.75 1977.27,1287.85 1978.23,1288.29 1979.18,1289.19 1980.14,1287.32 \n",
       "  1981.09,1287.5 1982.05,1287.02 1983,1283.64 1983.96,1281.39 1984.91,1279.61 1985.87,1277.95 1986.83,1276.87 1987.78,1272.98 1988.74,1269.13 1989.69,1268.68 \n",
       "  1990.65,1265.53 1991.6,1264.37 1992.56,1263.83 1993.51,1263.61 1994.47,1266.37 1995.42,1265.3 1996.38,1262.47 1997.34,1264.07 1998.29,1262.71 1999.25,1259.84 \n",
       "  2000.2,1259.6 2001.16,1259.12 2002.11,1257.83 2003.07,1254.69 2004.02,1252.79 2004.98,1249.89 2005.94,1250.46 2006.89,1250.39 2007.85,1251.32 2008.8,1250.73 \n",
       "  2009.76,1250.45 2010.71,1251.92 2011.67,1253.3 2012.62,1252.57 2013.58,1252.11 2014.54,1252.42 2015.49,1250.73 2016.45,1248.44 2017.4,1246.6 2018.36,1249.02 \n",
       "  2019.31,1248.24 2020.27,1247.76 2021.22,1245.61 2022.18,1244.39 2023.13,1243.55 2024.09,1244.73 2025.05,1243.94 2026,1240.5 2026.96,1236.03 2027.91,1237.18 \n",
       "  2028.87,1234.99 2029.82,1237.63 2030.78,1232.94 2031.73,1230.84 2032.69,1234.74 2033.65,1235.55 2034.6,1236.16 2035.56,1221.58 2036.51,1222.75 2037.47,1220.92 \n",
       "  2038.42,1221.77 2039.38,1215.6 2040.33,1212.38 2041.29,1205.2 2042.24,1202.92 2043.2,1202.1 2044.16,1197.96 2045.11,1200.84 2046.07,1204.23 2047.02,1199.9 \n",
       "  2047.98,1195.37 2048.93,1192.49 2049.89,1194.66 2050.84,1195.54 2051.8,1192.59 2052.76,1194.5 2053.71,1195.45 2054.67,1194.47 2055.62,1192.06 2056.58,1191.71 \n",
       "  2057.53,1192.44 2058.49,1191.48 2059.44,1190.78 2060.4,1191.18 2061.35,1186.77 2062.31,1195.06 2063.27,1196.91 2064.22,1200.85 2065.18,1200.5 2066.13,1200.93 \n",
       "  2067.09,1200.33 2068.04,1201.94 2069,1200.27 2069.95,1205.4 2070.91,1204.19 2071.87,1207.36 2072.82,1206.78 2073.78,1206.34 2074.73,1210.67 2075.69,1213.94 \n",
       "  2076.64,1213.03 2077.6,1209.13 2078.55,1207.61 2079.51,1206.73 2080.47,1209.2 2081.42,1207.83 2082.38,1208.71 2083.33,1209.63 2084.29,1209.45 2085.24,1207.4 \n",
       "  2086.2,1212.11 2087.15,1211.75 2088.11,1208.35 2089.06,1213.03 2090.02,1210.66 2090.98,1206.54 2091.93,1207.51 2092.89,1203.19 2093.84,1201.91 2094.8,1186.94 \n",
       "  2095.75,1186.28 2096.71,1188.27 2097.66,1187.56 2098.62,1186.78 2099.58,1187.82 2100.53,1183.15 2101.49,1188.63 2102.44,1191.61 2103.4,1189.6 2104.35,1186.7 \n",
       "  2105.31,1181.66 2106.26,1185.68 2107.22,1187.55 2108.17,1182.34 2109.13,1181.57 2110.09,1181.86 2111.04,1180.16 2112,1180.05 2112.95,1171.84 2113.91,1179.86 \n",
       "  2114.86,1183.92 2115.82,1180.36 2116.77,1185.39 2117.73,1179.83 2118.69,1191.46 2119.64,1191.59 2120.6,1194.41 2121.55,1189.34 2122.51,1182.33 2123.46,1183.66 \n",
       "  2124.42,1184.69 2125.37,1181.44 2126.33,1178.27 2127.28,1177.55 2128.24,1172.31 2129.2,1173.48 2130.15,1175.68 2131.11,1178.61 2132.06,1176.47 2133.02,1177 \n",
       "  2133.97,1176.56 2134.93,1175.58 2135.88,1171.32 2136.84,1168.05 2137.8,1165.72 2138.75,1163.42 2139.71,1162.36 2140.66,1162.7 2141.62,1159.43 2142.57,1165.22 \n",
       "  2143.53,1169.58 2144.48,1166.23 2145.44,1167.83 2146.4,1171.38 2147.35,1168.77 2148.31,1172.49 2149.26,1173.09 2150.22,1175.01 2151.17,1173.13 2152.13,1169.38 \n",
       "  2153.08,1167.77 2154.04,1173.51 2154.99,1162.6 2155.95,1158.12 2156.91,1162.42 2157.86,1162.17 2158.82,1158.87 2159.77,1152.94 2160.73,1153.58 2161.68,1155.08 \n",
       "  2162.64,1154.12 2163.59,1157.41 2164.55,1154.12 2165.51,1151.4 2166.46,1152.43 2167.42,1155.2 2168.37,1157.93 2169.33,1161.25 2170.28,1161.46 2171.24,1153.64 \n",
       "  2172.19,1153.66 2173.15,1154.36 2174.1,1157.76 2175.06,1158.1 2176.02,1153.1 2176.97,1156.42 2177.93,1158.1 2178.88,1154.29 2179.84,1149.27 2180.79,1148.11 \n",
       "  2181.75,1150.03 2182.7,1150.51 2183.66,1148.11 2184.62,1149.53 2185.57,1133.04 2186.53,1132.7 2187.48,1131.8 2188.44,1127.77 2189.39,1124.49 2190.35,1122.34 \n",
       "  2191.3,1125.84 2192.26,1124.65 2193.21,1127.41 2194.17,1129.24 2195.13,1128.77 2196.08,1129.46 2197.04,1131.1 2197.99,1131.57 2198.95,1125.16 2199.9,1127.42 \n",
       "  2200.86,1128.84 2201.81,1129.84 2202.77,1132.11 2203.73,1126.23 2204.68,1128.52 2205.64,1128.02 2206.59,1128.38 2207.55,1130.02 2208.5,1138.74 2209.46,1130.78 \n",
       "  2210.41,1138.57 2211.37,1130.08 2212.33,1138.12 2213.28,1129.83 2214.24,1139.68 2215.19,1143.02 2216.15,1139.11 2217.1,1136.1 2218.06,1133.77 2219.01,1129.59 \n",
       "  2219.97,1137.25 2220.92,1142.65 2221.88,1136.31 2222.84,1121.04 2223.79,1118.63 2224.75,1130.56 2225.7,1124.91 2226.66,1125.93 2227.61,1123.65 2228.57,1123.08 \n",
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       "  1092.47,1197.53 1093.43,1204.53 1094.38,1211.34 1095.34,1198.47 1096.29,1205.64 1097.25,1205.11 1098.2,1208.84 1099.16,1200.64 1100.11,1200.4 1101.07,1201.32 \n",
       "  1102.03,1202.1 1102.98,1201.16 1103.94,1203.41 1104.89,1203.61 1105.85,1211.71 1106.8,1210.2 1107.76,1216.24 1108.71,1216.98 1109.67,1211.37 1110.63,1214.11 \n",
       "  1111.58,1208.19 1112.54,1212.13 1113.49,1207.59 1114.45,1190.52 1115.4,1188.99 1116.36,1194.35 1117.31,1200.77 1118.27,1199.4 1119.23,1198.95 1120.18,1202.02 \n",
       "  1121.14,1206.57 1122.09,1202.77 1123.05,1191.08 1124,1183.97 1124.96,1183.06 1125.91,1188.38 1126.87,1192.87 1127.82,1189.91 1128.78,1189.54 1129.74,1187.77 \n",
       "  1130.69,1185.8 1131.65,1185.95 1132.6,1181.01 1133.56,1172.87 1134.51,1165.78 1135.47,1157.38 1136.42,1154.97 1137.38,1156.92 1138.34,1149.61 1139.29,1147.97 \n",
       "  1140.25,1154.06 1141.2,1171.86 1142.16,1163.41 1143.11,1161.21 1144.07,1166.87 1145.02,1177.6 1145.98,1168.18 1146.93,1165.26 1147.89,1164.95 1148.85,1160.91 \n",
       "  1149.8,1169.08 1150.76,1161.78 1151.71,1164.05 1152.67,1155.69 1153.62,1146.76 1154.58,1148.83 1155.53,1142.76 1156.49,1138.58 1157.45,1140.67 1158.4,1141.82 \n",
       "  1159.36,1140.68 1160.31,1144.5 1161.27,1149.69 1162.22,1149.44 1163.18,1142.56 1164.13,1135.86 1165.09,1135.84 1166.04,1138.88 1167,1137.59 1167.96,1146.58 \n",
       "  1168.91,1148.37 1169.87,1153.24 1170.82,1151.06 1171.78,1160.16 1172.73,1150.48 1173.69,1151.54 1174.64,1159.48 1175.6,1158.23 1176.56,1156.79 1177.51,1153.08 \n",
       "  1178.47,1148.2 1179.42,1146.93 1180.38,1147.42 1181.33,1159.38 1182.29,1168.3 1183.24,1177 1184.2,1177.07 1185.15,1172.77 1186.11,1174.74 1187.07,1172.91 \n",
       "  1188.02,1178.73 1188.98,1165.86 1189.93,1170.46 1190.89,1170 1191.84,1172.27 1192.8,1178.13 1193.75,1174.58 1194.71,1175.47 1195.67,1170.96 1196.62,1164.41 \n",
       "  1197.58,1166.51 1198.53,1166.69 1199.49,1164.39 1200.44,1165.78 1201.4,1162.81 1202.35,1161.13 1203.31,1159.97 1204.27,1164.05 1205.22,1164.44 1206.18,1167.69 \n",
       "  1207.13,1165.9 1208.09,1176.25 1209.04,1184.76 1210,1182.33 1210.95,1187.17 1211.91,1189.32 1212.86,1195.98 1213.82,1204.96 1214.78,1205.52 1215.73,1201.63 \n",
       "  1216.69,1205.13 1217.64,1207.19 1218.6,1208.28 1219.55,1206.07 1220.51,1205.27 1221.46,1181.5 1222.42,1185.74 1223.38,1183.89 1224.33,1181.47 1225.29,1180.32 \n",
       "  1226.24,1182.68 1227.2,1176.29 1228.15,1178.41 1229.11,1190.3 1230.06,1189.31 1231.02,1194.16 1231.97,1190.06 1232.93,1194.5 1233.89,1195 1234.84,1180.95 \n",
       "  1235.8,1180.85 1236.75,1180.83 1237.71,1180.25 1238.66,1180.61 1239.62,1183.53 1240.57,1196.43 1241.53,1204.12 1242.49,1196.06 1243.44,1196.85 1244.4,1193.33 \n",
       "  1245.35,1193.22 1246.31,1199.89 1247.26,1178.66 1248.22,1177.63 1249.17,1191.09 1250.13,1208.17 1251.08,1202.17 1252.04,1201.22 1253,1217.99 1253.95,1235.65 \n",
       "  1254.91,1229.19 1255.86,1233.17 1256.82,1236.86 1257.77,1231.65 1258.73,1229.46 1259.68,1229.52 1260.64,1230.64 1261.6,1232.64 1262.55,1240.5 1263.51,1230 \n",
       "  1264.46,1234.26 1265.42,1232.68 1266.37,1229.95 1267.33,1244.76 1268.28,1241.27 1269.24,1249.06 1270.2,1246.76 1271.15,1238.5 1272.11,1234.37 1273.06,1217.45 \n",
       "  1274.02,1213.23 1274.97,1223.18 1275.93,1204.7 1276.88,1203.85 1277.84,1207.16 1278.79,1212.26 1279.75,1209.16 1280.71,1210.09 1281.66,1204.42 1282.62,1209.23 \n",
       "  1283.57,1211.03 1284.53,1206.31 1285.48,1206.98 1286.44,1202.13 1287.39,1197.02 1288.35,1187.73 1289.31,1188.52 1290.26,1180.66 1291.22,1168.99 1292.17,1171.37 \n",
       "  1293.13,1159.57 1294.08,1165.32 1295.04,1161.41 1295.99,1167.39 1296.95,1168.74 1297.9,1156.4 1298.86,1148.73 1299.82,1142.15 1300.77,1152.31 1301.73,1151.13 \n",
       "  1302.68,1154.83 1303.64,1149.41 1304.59,1158 1305.55,1153.85 1306.5,1170.9 1307.46,1177.05 1308.42,1188.88 1309.37,1190.49 1310.33,1192.33 1311.28,1170.91 \n",
       "  1312.24,1171.09 1313.19,1178.21 1314.15,1167.74 1315.1,1164.63 1316.06,1152.14 1317.01,1163.01 1317.97,1164.56 1318.93,1166.73 1319.88,1163.77 1320.84,1161.73 \n",
       "  1321.79,1173.4 1322.75,1162.44 1323.7,1153.51 1324.66,1157.13 1325.61,1152 1326.57,1146.48 1327.53,1146.63 1328.48,1150.92 1329.44,1157.26 1330.39,1155.1 \n",
       "  1331.35,1157.64 1332.3,1169.08 1333.26,1167.58 1334.21,1177.74 1335.17,1175.78 1336.13,1185.96 1337.08,1186.54 1338.04,1191.53 1338.99,1177.87 1339.95,1172.44 \n",
       "  1340.9,1167.3 1341.86,1170.14 1342.81,1176.27 1343.77,1176.56 1344.72,1172.94 1345.68,1178 1346.64,1183.99 1347.59,1185 1348.55,1182.4 1349.5,1165.78 \n",
       "  1350.46,1161.73 1351.41,1138.27 1352.37,1159.29 1353.32,1171.38 1354.28,1194.08 1355.24,1159.34 1356.19,1157.62 1357.15,1158.84 1358.1,1157.59 1359.06,1167.84 \n",
       "  1360.01,1163.22 1360.97,1172.72 1361.92,1164.84 1362.88,1167.35 1363.83,1170.52 1364.79,1159.55 1365.75,1156.1 1366.7,1156.35 1367.66,1166.83 1368.61,1172.97 \n",
       "  1369.57,1162.13 1370.52,1165.59 1371.48,1163.37 1372.43,1162.67 1373.39,1157.69 1374.35,1163.19 1375.3,1155.06 1376.26,1177.09 1377.21,1168.99 1378.17,1175.54 \n",
       "  1379.12,1161.03 1380.08,1158.98 1381.03,1155.06 1381.99,1164.08 1382.94,1167.77 1383.9,1182.01 1384.86,1185.31 1385.81,1181.68 1386.77,1181.45 1387.72,1191.64 \n",
       "  1388.68,1207.95 1389.63,1218.88 1390.59,1220.39 1391.54,1212.43 1392.5,1207.14 1393.46,1213.89 1394.41,1224.76 1395.37,1212.25 1396.32,1215.98 1397.28,1188.23 \n",
       "  1398.23,1168.86 1399.19,1162.06 1400.14,1162.6 1401.1,1155.97 1402.06,1160.12 1403.01,1145.39 1403.97,1135.35 1404.92,1144.7 1405.88,1128.75 1406.83,1131.94 \n",
       "  1407.79,1136.38 1408.74,1127.58 1409.7,1136.94 1410.65,1136.31 1411.61,1137.1 1412.57,1136.11 1413.52,1132.53 1414.48,1141.5 1415.43,1133.66 1416.39,1135.26 \n",
       "  1417.34,1130.79 1418.3,1139.11 1419.25,1130.03 1420.21,1141.36 1421.17,1120.41 1422.12,1125.62 1423.08,1113.56 1424.03,1119.55 1424.99,1119.78 1425.94,1129.6 \n",
       "  1426.9,1126.85 1427.85,1126.06 1428.81,1132.69 1429.76,1143.62 1430.72,1139.65 1431.68,1135.57 1432.63,1133.08 1433.59,1124.33 1434.54,1131.42 1435.5,1118.05 \n",
       "  1436.45,1116.68 1437.41,1121.74 1438.36,1132.76 1439.32,1126.34 1440.28,1107.8 1441.23,1094.57 1442.19,1080.57 1443.14,1071 1444.1,1081.12 1445.05,1093.56 \n",
       "  1446.01,1101.39 1446.96,1086.6 1447.92,1061.9 1448.87,1080.14 1449.83,1076.95 1450.79,1072.68 1451.74,1079.6 1452.7,1083.21 1453.65,1068.66 1454.61,1075.89 \n",
       "  1455.56,1082.33 1456.52,1074.82 1457.47,1063.13 1458.43,1071.89 1459.39,1076.1 1460.34,1079.54 1461.3,1069.56 1462.25,1103.99 1463.21,1091.77 1464.16,1095.29 \n",
       "  1465.12,1083.87 1466.07,1068.49 1467.03,1068.74 1467.99,1073.37 1468.94,1057.95 1469.9,1052.9 1470.85,1084.7 1471.81,1079.78 1472.76,1069.74 1473.72,1048.67 \n",
       "  1474.67,1053.94 1475.63,1100.95 1476.58,1111.87 1477.54,1141.39 1478.5,1144.01 1479.45,1162.67 1480.41,1149.33 1481.36,1157.94 1482.32,1162.93 1483.27,1157.47 \n",
       "  1484.23,1156.49 1485.18,1155.97 1486.14,1156.71 1487.1,1161.33 1488.05,1143.92 1489.01,1148.02 1489.96,1164.55 1490.92,1153.03 1491.87,1144.64 1492.83,1147.05 \n",
       "  1493.78,1133.78 1494.74,1131.82 1495.69,1130.81 1496.65,1130.09 1497.61,1136.07 1498.56,1139.68 1499.52,1141 1500.47,1137.51 1501.43,1148.82 1502.38,1156.63 \n",
       "  1503.34,1154.41 1504.29,1150.78 1505.25,1153.73 1506.21,1146.04 1507.16,1139.22 1508.12,1140.48 1509.07,1145.65 1510.03,1157.32 1510.98,1149.29 1511.94,1143.17 \n",
       "  1512.89,1127.08 1513.85,1140.38 1514.8,1121.5 1515.76,1126.69 1516.72,1150.7 1517.67,1129.26 1518.63,1163.22 1519.58,1176.4 1520.54,1186.39 1521.49,1191.58 \n",
       "  1522.45,1165.12 1523.4,1169.1 1524.36,1178.47 1525.32,1177.56 1526.27,1184.77 1527.23,1194.61 1528.18,1198.46 1529.14,1210.36 1530.09,1195.4 1531.05,1201.74 \n",
       "  1532,1217.1 1532.96,1229.03 1533.92,1209.4 1534.87,1220.79 1535.83,1255.74 1536.78,1233.16 1537.74,1221.82 1538.69,1209.02 1539.65,1230.61 1540.6,1252.37 \n",
       "  1541.56,1271.2 1542.51,1279.08 1543.47,1279.93 1544.43,1239.58 1545.38,1227.37 1546.34,1198.96 1547.29,1200.04 1548.25,1206.33 1549.2,1212.6 1550.16,1229.61 \n",
       "  1551.11,1238.44 1552.07,1254.41 1553.03,1267.59 1553.98,1272.15 1554.94,1291.65 1555.89,1270.54 1556.85,1285.28 1557.8,1283.42 1558.76,1293.97 1559.71,1293.83 \n",
       "  1560.67,1292.69 1561.62,1270.77 1562.58,1257.89 1563.54,1246.36 1564.49,1230.88 1565.45,1229.77 1566.4,1253.25 1567.36,1243 1568.31,1232.29 1569.27,1214.93 \n",
       "  1570.22,1199.16 1571.18,1194.76 1572.14,1221.64 1573.09,1232.33 1574.05,1239.59 1575,1228.57 1575.96,1235.69 1576.91,1226.55 1577.87,1207.41 1578.82,1190.35 \n",
       "  1579.78,1188.96 1580.73,1209.14 1581.69,1218.46 1582.65,1218.35 1583.6,1210.85 1584.56,1215.57 1585.51,1211.02 1586.47,1200.1 1587.42,1189.86 1588.38,1192.42 \n",
       "  1589.33,1204.75 1590.29,1208.41 1591.25,1206.41 1592.2,1210.46 1593.16,1196.26 1594.11,1194.34 1595.07,1210.09 1596.02,1181.37 1596.98,1167.88 1597.93,1156.1 \n",
       "  1598.89,1170.23 1599.85,1137.65 1600.8,1155.09 1601.76,1162.39 1602.71,1180.08 1603.67,1165.74 1604.62,1173.25 1605.58,1167.23 1606.53,1160.56 1607.49,1135.56 \n",
       "  1608.44,1152.59 1609.4,1139.28 1610.36,1154.45 1611.31,1181.28 1612.27,1186.03 1613.22,1203.21 1614.18,1175.81 1615.13,1179.41 1616.09,1182.43 1617.04,1168.42 \n",
       "  1618,1151.32 1618.96,1145.42 1619.91,1166.92 1620.87,1166.52 1621.82,1189.08 1622.78,1203.89 1623.73,1168.83 1624.69,1183.68 1625.64,1184.7 1626.6,1173.51 \n",
       "  1627.55,1175.85 1628.51,1177.51 1629.47,1220.64 1630.42,1224.29 1631.38,1222.43 1632.33,1212.05 1633.29,1198.03 1634.24,1208 1635.2,1194.19 1636.15,1207.74 \n",
       "  1637.11,1190.33 1638.07,1185.04 1639.02,1176.82 1639.98,1190.28 1640.93,1191.57 1641.89,1176.3 1642.84,1180.7 1643.8,1171.26 1644.75,1192.66 1645.71,1190.83 \n",
       "  1646.66,1160.08 1647.62,1155.79 1648.58,1161.37 1649.53,1169.49 1650.49,1149.21 1651.44,1171.89 1652.4,1193.3 1653.35,1211.35 1654.31,1192.74 1655.26,1189.44 \n",
       "  1656.22,1176.2 1657.18,1172.45 1658.13,1181.36 1659.09,1148.5 1660.04,1146.29 1661,1152.19 1661.95,1152.08 1662.91,1133.96 1663.86,1155.82 1664.82,1156.74 \n",
       "  1665.78,1167.52 1666.73,1165.03 1667.69,1169.56 1668.64,1190.91 1669.6,1216.04 1670.55,1210.56 1671.51,1212.33 1672.46,1217.88 1673.42,1221.94 1674.37,1220.58 \n",
       "  1675.33,1214.36 1676.29,1209.82 1677.24,1199.11 1678.2,1200.08 1679.15,1190.03 1680.11,1181.72 1681.06,1165.29 1682.02,1164.5 1682.97,1162.32 1683.93,1135.45 \n",
       "  1684.89,1134.83 1685.84,1149.23 1686.8,1144.15 1687.75,1152.3 1688.71,1155.49 1689.66,1157.22 1690.62,1153.03 1691.57,1168.24 1692.53,1190.16 1693.48,1191.95 \n",
       "  1694.44,1194.99 1695.4,1196.71 1696.35,1192.49 1697.31,1183.78 1698.26,1185.63 1699.22,1185.61 1700.17,1192.78 1701.13,1199.25 1702.08,1196.62 1703.04,1205.27 \n",
       "  1704,1204.87 1704.95,1219 1705.91,1219.34 1706.86,1229.75 1707.82,1212.28 1708.77,1224.87 1709.73,1216.2 1710.68,1213.51 1711.64,1217.78 1712.59,1220.13 \n",
       "  1713.55,1220.44 1714.51,1218.69 1715.46,1218.36 1716.42,1222.04 1717.37,1210.49 1718.33,1217.98 1719.28,1198.82 1720.24,1219.66 1721.19,1209.15 1722.15,1218.67 \n",
       "  1723.11,1219.5 1724.06,1212.86 1725.02,1202.21 1725.97,1206.92 1726.93,1212.69 1727.88,1208.9 1728.84,1216.88 1729.79,1218.37 1730.75,1199.21 1731.71,1202.63 \n",
       "  1732.66,1203.48 1733.62,1197.62 1734.57,1205.39 1735.53,1213.53 1736.48,1220.74 1737.44,1221.12 1738.39,1212.41 1739.35,1211.09 1740.3,1216.3 1741.26,1218.94 \n",
       "  1742.22,1222.19 1743.17,1215.44 1744.13,1206.55 1745.08,1217.93 1746.04,1225.28 1746.99,1224.68 1747.95,1228.74 1748.9,1216.39 1749.86,1211.55 1750.82,1197.83 \n",
       "  1751.77,1193.24 1752.73,1194.81 1753.68,1191.31 1754.64,1188.72 1755.59,1194.52 1756.55,1186.96 1757.5,1185.43 1758.46,1178.95 1759.41,1178.23 1760.37,1182.13 \n",
       "  1761.33,1186.26 1762.28,1184.73 1763.24,1177.15 1764.19,1178.15 1765.15,1170.58 1766.1,1148.46 1767.06,1162.58 1768.01,1163.9 1768.97,1160.03 1769.93,1156.88 \n",
       "  1770.88,1158.18 1771.84,1168.23 1772.79,1175.69 1773.75,1181.71 1774.7,1181.32 1775.66,1183.12 1776.61,1178.5 1777.57,1169.52 1778.52,1161.26 1779.48,1168.49 \n",
       "  1780.44,1169.94 1781.39,1169.99 1782.35,1188.5 1783.3,1185.13 1784.26,1185.9 1785.21,1177.62 1786.17,1167.88 1787.12,1172.94 1788.08,1165.61 1789.04,1160.9 \n",
       "  1789.99,1164.84 1790.95,1148.65 1791.9,1138.65 1792.86,1134.57 1793.81,1136.14 1794.77,1136.93 1795.72,1133.55 1796.68,1126.9 1797.63,1115.35 1798.59,1125.19 \n",
       "  1799.55,1133.38 1800.5,1129.69 1801.46,1126.6 1802.41,1120.12 1803.37,1117.63 1804.32,1105.24 1805.28,1108.19 1806.23,1109.18 1807.19,1113.91 1808.15,1110.21 \n",
       "  1809.1,1130.08 1810.06,1138.22 1811.01,1131.02 1811.97,1128.42 1812.92,1137.13 1813.88,1120.87 1814.83,1116.81 1815.79,1113.1 1816.75,1109.05 1817.7,1105.61 \n",
       "  1818.66,1110.07 1819.61,1100.91 1820.57,1104.26 1821.52,1097.19 1822.48,1094.98 1823.43,1097.34 1824.39,1100.18 1825.34,1099.98 1826.3,1100.79 1827.26,1104.07 \n",
       "  1828.21,1120.36 1829.17,1116.88 1830.12,1124.65 1831.08,1122.61 1832.03,1131.9 1832.99,1136.5 1833.94,1131.93 1834.9,1131.04 1835.86,1148.56 1836.81,1144.46 \n",
       "  1837.77,1143.84 1838.72,1153.07 1839.68,1142.87 1840.63,1140.62 1841.59,1144.24 1842.54,1139.63 1843.5,1148.9 1844.45,1170.09 1845.41,1167.76 1846.37,1161.92 \n",
       "  1847.32,1160.27 1848.28,1163.71 1849.23,1173.31 1850.19,1181.3 1851.14,1180.99 1852.1,1171.86 1853.05,1169.79 1854.01,1167.65 1854.97,1165.65 1855.92,1161.07 \n",
       "  1856.88,1157.32 1857.83,1162.54 1858.79,1164.44 1859.74,1173.24 1860.7,1171.73 1861.65,1171.23 1862.61,1174.8 1863.56,1173.85 1864.52,1175.69 1865.48,1163.67 \n",
       "  1866.43,1166.12 1867.39,1160.28 1868.34,1161.36 1869.3,1164.49 1870.25,1166.84 1871.21,1161.7 1872.16,1157.25 1873.12,1154.45 1874.08,1150.3 1875.03,1151.27 \n",
       "  1875.99,1152.2 1876.94,1134.38 1877.9,1132.1 1878.85,1129.08 1879.81,1132.29 1880.76,1143.32 1881.72,1139.98 1882.68,1138.84 1883.63,1139.56 1884.59,1144.62 \n",
       "  1885.54,1142.92 1886.5,1136.34 1887.45,1131.48 1888.41,1133.34 1889.36,1136.89 1890.32,1134.99 1891.27,1133.04 1892.23,1135.19 1893.19,1135.64 1894.14,1145.69 \n",
       "  1895.1,1159.01 1896.05,1155.05 1897.01,1151.22 1897.96,1151.13 1898.92,1150.8 1899.87,1146.87 1900.83,1152.82 1901.79,1152.68 1902.74,1161.02 1903.7,1159.34 \n",
       "  1904.65,1155.91 1905.61,1161.73 1906.56,1152.6 1907.52,1150.37 1908.47,1152.29 1909.43,1162.72 1910.38,1162.22 1911.34,1149.57 1912.3,1146.33 1913.25,1143.54 \n",
       "  1914.21,1143.18 1915.16,1147.96 1916.12,1141.17 1917.07,1142.25 1918.03,1146.55 1918.98,1148.79 1919.94,1141.82 1920.9,1141.04 1921.85,1138.8 1922.81,1140.68 \n",
       "  1923.76,1130.29 1924.72,1123.46 1925.67,1125.49 1926.63,1107.28 1927.58,1108.25 1928.54,1122.34 1929.49,1122.07 1930.45,1111.45 1931.41,1100.69 1932.36,1091.9 \n",
       "  1933.32,1094.22 1934.27,1094.26 1935.23,1082.99 1936.18,1088.12 1937.14,1081.56 1938.09,1084.46 1939.05,1082.05 1940.01,1086.83 1940.96,1079.6 1941.92,1096.07 \n",
       "  1942.87,1090.53 1943.83,1095.58 1944.78,1110.27 1945.74,1120.69 1946.69,1112.99 1947.65,1109.27 1948.61,1127.48 1949.56,1128.79 1950.52,1107.54 1951.47,1108.13 \n",
       "  1952.43,1113.49 1953.38,1108.25 1954.34,1115.38 1955.29,1114.26 1956.25,1108 1957.2,1104.81 1958.16,1101.67 1959.12,1103.16 1960.07,1090 1961.03,1074.3 \n",
       "  1961.98,1079.02 1962.94,1067.69 1963.89,1071.38 1964.85,1067.71 1965.8,1060.78 1966.76,1069.55 1967.72,1073.78 1968.67,1062.68 1969.63,1063.94 1970.58,1063.69 \n",
       "  1971.54,1057.54 1972.49,1039.41 1973.45,1051.91 1974.4,1033.08 1975.36,1047.52 1976.31,1054.46 1977.27,1043.01 1978.23,1044.79 1979.18,1048.42 1980.14,1040.99 \n",
       "  1981.09,1041.73 1982.05,1039.82 1983,1026.32 1983.96,1017.18 1984.91,1009.89 1985.87,1003.1 1986.83,998.597 1987.78,982.422 1988.74,966.114 1989.69,964.237 \n",
       "  1990.65,950.689 1991.6,945.676 1992.56,943.342 1993.51,942.415 1994.47,954.52 1995.42,949.895 1996.38,937.6 1997.34,944.654 1998.29,938.739 1999.25,926.137 \n",
       "  2000.2,925.091 2001.16,922.99 2002.11,917.288 2003.07,903.277 2004.02,894.689 2004.98,881.5 2005.94,884.165 2006.89,883.845 2007.85,888.16 2008.8,885.483 \n",
       "  2009.76,884.208 2010.71,891.004 2011.67,897.317 2012.62,894.037 2013.58,891.966 2014.54,893.414 2015.49,885.749 2016.45,875.262 2017.4,866.778 2018.36,878.06 \n",
       "  2019.31,874.515 2020.27,872.311 2021.22,862.369 2022.18,856.733 2023.13,852.805 2024.09,858.384 2025.05,854.696 2026,838.588 2026.96,817.388 2027.91,822.972 \n",
       "  2028.87,812.469 2029.82,825.284 2030.78,802.844 2031.73,792.652 2032.69,811.809 2033.65,815.759 2034.6,818.697 2035.56,748.546 2036.51,754.451 2037.47,745.319 \n",
       "  2038.42,749.617 2039.38,718.583 2040.33,702.058 2041.29,664.886 2042.24,652.815 2043.2,648.452 2044.16,626.315 2045.11,641.987 2046.07,660.252 2047.02,637.26 \n",
       "  2047.98,612.908 2048.93,597.21 2049.89,609.176 2050.84,614.063 2051.8,598.024 2052.76,608.562 2053.71,613.784 2054.67,608.459 2055.62,595.357 2056.58,593.448 \n",
       "  2057.53,597.536 2058.49,592.246 2059.44,588.464 2060.4,590.705 2061.35,566.384 2062.31,612.792 2063.27,622.914 2064.22,644.336 2065.18,642.489 2066.13,644.857 \n",
       "  2067.09,641.677 2068.04,650.339 2069,641.453 2069.95,669.041 2070.91,662.709 2071.87,679.551 2072.82,676.512 2073.78,674.265 2074.73,697.056 2075.69,714.075 \n",
       "  2076.64,709.433 2077.6,689.363 2078.55,681.518 2079.51,676.918 2080.47,689.924 2081.42,682.832 2082.38,687.48 2083.33,692.337 2084.29,691.398 2085.24,680.79 \n",
       "  2086.2,705.491 2087.15,703.685 2088.11,686.106 2089.06,710.627 2090.02,698.453 2090.98,677.14 2091.93,682.271 2092.89,659.659 2093.84,652.936 2094.8,573.266 \n",
       "  2095.75,569.641 2096.71,580.768 2097.66,576.868 2098.62,572.595 2099.58,578.39 2100.53,552.558 2101.49,583.371 2102.44,599.903 2103.4,588.951 2104.35,573.012 \n",
       "  2105.31,545.042 2106.26,567.755 2107.22,578.177 2108.17,549.381 2109.13,545.063 2110.09,546.767 2111.04,537.216 2112,536.685 2112.95,490.247 2113.91,536.698 \n",
       "  2114.86,559.733 2115.82,539.889 2116.77,568.324 2117.73,537.418 2118.69,603.159 2119.64,603.903 2120.6,619.321 2121.55,591.963 2122.51,553.567 2123.46,561.032 \n",
       "  2124.42,566.837 2125.37,548.782 2126.33,531.061 2127.28,526.997 2128.24,497.34 2129.2,504.084 2130.15,516.787 2131.11,533.514 2132.06,521.446 2133.02,524.545 \n",
       "  2133.97,522.042 2134.93,516.533 2135.88,492.264 2136.84,473.493 2137.8,459.956 2138.75,446.504 2139.71,440.295 2140.66,442.358 2141.62,423.126 2142.57,457.65 \n",
       "  2143.53,483.25 2144.48,463.898 2145.44,473.321 2146.4,494.009 2147.35,479.007 2148.31,500.649 2149.26,504.131 2150.22,515.172 2151.17,504.53 2152.13,483.075 \n",
       "  2153.08,473.801 2154.04,507.188 2154.99,444.829 2155.95,418.475 2156.91,444.183 2157.86,442.766 2158.82,423.366 2159.77,388.139 2160.73,392.012 2161.68,401.136 \n",
       "  2162.64,395.417 2163.59,415.254 2164.55,395.684 2165.51,379.363 2166.46,385.663 2167.42,402.452 2168.37,418.913 2169.33,438.726 2170.28,440.023 2171.24,393.908 \n",
       "  2172.19,394.099 2173.15,398.329 2174.1,418.83 2175.06,420.93 2176.02,391.192 2176.97,411.288 2177.93,421.384 2178.88,398.74 2179.84,368.62 2180.79,361.64 \n",
       "  2181.75,373.378 2182.7,376.361 2183.66,361.841 2184.62,370.56 2185.57,270.329 2186.53,268.213 2187.48,262.589 2188.44,237.001 2189.39,216.026 2190.35,202.131 \n",
       "  2191.3,224.986 2192.26,217.386 2193.21,235.234 2194.17,247.073 2195.13,244.107 2196.08,248.575 2197.04,259.111 2197.99,262.2 2198.95,221.509 2199.9,236.167 \n",
       "  2200.86,245.297 2201.81,251.768 2202.77,266.33 2203.73,229.082 2204.68,243.86 2205.64,240.739 2206.59,243.086 2207.55,253.648 2208.5,309.247 2209.46,259.7 \n",
       "  2210.41,309.269 2211.37,256.457 2212.33,307.646 2213.28,256.051 2214.24,318.756 2215.19,339.493 2216.15,315.555 2217.1,296.923 2218.06,282.429 2219.01,256.146 \n",
       "  2219.97,304.909 2220.92,338.563 2221.88,299.708 2222.84,204.485 2223.79,188.934 2224.75,266.665 2225.7,231.072 2226.66,237.647 2227.61,223.108 2228.57,219.52 \n",
       "  2229.52,208.278 2230.48,207.539 2231.44,199.869 2232.39,170.064 2233.35,190.684 2234.3,245.281 2235.26,251.04 2236.21,218.605 2237.17,191.918 2238.12,199.259 \n",
       "  2239.08,158.436 2240.03,115.935 2240.99,129.956 2241.95,124.229 2242.9,136.625 2243.86,136.733 2244.81,135.254 2245.77,98.5595 2246.72,103.432 2247.68,137.062 \n",
       "  2248.63,154.184 2249.59,164.4 2250.55,157.001 2251.5,155.604 2252.46,216.495 2253.41,206.157 2254.37,170.311 2255.32,188.101 2256.28,183.156 2257.23,159.343 \n",
       "  2258.19,120.31 2259.14,128.559 2260.1,142.926 2261.06,182.845 2262.01,184.605 2262.97,135.664 2263.92,161.63 2264.88,201.428 2265.83,180.322 2266.79,188.042 \n",
       "  2267.74,189.641 2268.7,198.692 2269.66,189.102 2270.61,175.822 2271.57,149.103 2272.52,88.0053 2273.48,96.9768 2274.43,112.36 2275.39,137.772 2276.34,162.467 \n",
       "  2277.3,152.832 2278.26,155.395 2279.21,150.088 2280.17,193.072 2281.12,215.105 2282.08,200.158 2283.03,187.126 2283.99,152.096 2284.94,161.556 2285.9,194.101 \n",
       "  2286.85,139.853 2287.81,96.3281 2288.77,126.651 2289.72,116.919 2290.68,105.107 2291.63,125.728 2292.59,137.608 2293.54,158.402 2294.5,146.356 2295.45,130.537 \n",
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       "  394.951,1445.17 395.906,1445.15 396.862,1445.15 397.817,1445.22 398.773,1445.22 399.728,1445.19 400.684,1445.19 401.639,1445.36 402.595,1445.42 403.55,1445.44 \n",
       "  404.506,1445.35 405.461,1445.5 406.417,1445.56 407.372,1445.54 408.328,1445.58 409.283,1445.65 410.239,1445.75 411.194,1445.67 412.15,1445.65 413.105,1445.72 \n",
       "  414.061,1445.72 415.016,1445.75 415.972,1445.74 416.927,1445.84 417.883,1445.88 418.838,1445.87 419.794,1445.88 420.749,1445.87 421.705,1445.88 422.66,1445.92 \n",
       "  423.616,1445.89 424.571,1445.89 425.527,1445.94 426.482,1446 427.438,1446.05 428.393,1446.06 429.349,1445.96 430.304,1445.94 431.26,1445.9 432.215,1445.86 \n",
       "  433.171,1445.87 434.126,1445.93 435.082,1445.96 436.037,1445.9 436.993,1445.87 437.948,1445.85 438.904,1445.75 439.86,1445.73 440.815,1445.81 441.771,1445.84 \n",
       "  442.726,1445.91 443.682,1445.89 444.637,1445.9 445.593,1445.94 446.548,1445.92 447.504,1445.94 448.459,1445.95 449.415,1445.91 450.37,1445.86 451.326,1445.87 \n",
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       "  461.836,1445.74 462.792,1445.75 463.747,1445.71 464.703,1445.69 465.658,1445.75 466.614,1445.63 467.569,1445.46 468.525,1445.47 469.48,1445.41 470.436,1445.39 \n",
       "  471.391,1445.42 472.347,1445.45 473.302,1445.39 474.258,1445.44 475.213,1445.42 476.169,1445.42 477.124,1445.46 478.08,1445.51 479.035,1445.56 479.991,1445.51 \n",
       "  480.946,1445.56 481.902,1445.56 482.857,1445.61 483.813,1445.62 484.768,1445.63 485.724,1445.55 486.679,1445.55 487.635,1445.6 488.59,1445.63 489.546,1445.66 \n",
       "  490.501,1445.67 491.457,1445.65 492.412,1445.66 493.368,1445.67 494.323,1445.64 495.279,1445.62 496.234,1445.63 497.19,1445.61 498.145,1445.63 499.101,1445.71 \n",
       "  500.056,1445.75 501.012,1445.72 501.967,1445.76 502.923,1445.81 503.878,1445.85 504.834,1445.83 505.789,1445.84 506.745,1445.75 507.701,1445.75 508.656,1445.74 \n",
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       "  557.387,1446.15 558.342,1446.17 559.298,1446.23 560.253,1446.21 561.209,1446.22 562.164,1446.22 563.12,1446.22 564.075,1446.25 565.031,1446.32 565.986,1446.29 \n",
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       "  796.264,1445.73 797.219,1445.65 798.175,1445.63 799.13,1445.73 800.086,1445.78 801.041,1445.8 801.997,1445.82 802.952,1445.79 803.908,1445.8 804.863,1445.85 \n",
       "  805.819,1445.9 806.774,1445.95 807.73,1445.92 808.685,1445.96 809.641,1445.96 810.596,1445.96 811.552,1445.97 812.507,1445.87 813.463,1445.88 814.418,1445.93 \n",
       "  815.374,1445.92 816.329,1445.86 817.285,1445.96 818.24,1445.98 819.196,1446.04 820.151,1446.12 821.107,1446.1 822.062,1446.07 823.018,1445.95 823.973,1445.94 \n",
       "  824.929,1445.96 825.884,1445.99 826.84,1446.02 827.795,1446.12 828.751,1446.15 829.706,1446.1 830.662,1446.03 831.617,1446.03 832.573,1446.14 833.528,1446.1 \n",
       "  834.484,1446.08 835.439,1446.04 836.395,1446.08 837.35,1446.13 838.306,1446.16 839.261,1446.13 840.217,1446.08 841.172,1446.1 842.128,1446.1 843.083,1446.04 \n",
       "  844.039,1446.01 844.994,1445.95 845.95,1445.92 846.906,1445.98 847.861,1446 848.817,1446.01 849.772,1445.99 850.728,1445.93 851.683,1445.93 852.639,1445.95 \n",
       "  853.594,1445.99 854.55,1446.05 855.505,1446.01 856.461,1445.96 857.416,1445.9 858.372,1445.93 859.327,1445.9 860.283,1445.92 861.238,1445.92 862.194,1445.94 \n",
       "  863.149,1445.94 864.105,1445.94 865.06,1445.9 866.016,1445.87 866.971,1445.89 867.927,1445.87 868.882,1445.91 869.838,1445.93 870.793,1445.97 871.749,1446.02 \n",
       "  872.704,1446.02 873.66,1446.06 874.615,1446.03 875.571,1446.15 876.526,1446.19 877.482,1446.15 878.437,1446.17 879.393,1446.27 880.348,1446.28 881.304,1446.31 \n",
       "  882.259,1446.37 883.215,1446.31 884.17,1446.32 885.126,1446.34 886.081,1446.5 887.037,1446.5 887.992,1446.57 888.948,1446.53 889.903,1446.52 890.859,1446.45 \n",
       "  891.814,1446.46 892.77,1446.43 893.725,1446.47 894.681,1446.49 895.636,1446.57 896.592,1446.58 897.547,1446.55 898.503,1446.65 899.458,1446.6 900.414,1446.58 \n",
       "  901.369,1446.65 902.325,1446.52 903.28,1446.53 904.236,1446.56 905.191,1446.56 906.147,1446.57 907.102,1446.5 908.058,1446.55 909.013,1446.55 909.969,1446.53 \n",
       "  910.924,1446.53 911.88,1446.59 912.835,1446.57 913.791,1446.58 914.747,1446.6 915.702,1446.57 916.658,1446.51 917.613,1446.53 918.569,1446.49 919.524,1446.5 \n",
       "  920.48,1446.46 921.435,1446.45 922.391,1446.51 923.346,1446.46 924.302,1446.5 925.257,1446.54 926.213,1446.56 927.168,1446.51 928.124,1446.53 929.079,1446.52 \n",
       "  930.035,1446.44 930.99,1446.38 931.946,1446.38 932.901,1446.38 933.857,1446.34 934.812,1446.38 935.768,1446.4 936.723,1446.41 937.679,1446.35 938.634,1446.37 \n",
       "  939.59,1446.3 940.545,1446.2 941.501,1446.18 942.456,1446.21 943.412,1446.2 944.367,1446.19 945.323,1446.19 946.278,1446.22 947.234,1446.29 948.189,1446.26 \n",
       "  949.145,1446.27 950.1,1446.3 951.056,1446.21 952.011,1446.15 952.967,1446.13 953.922,1446.16 954.878,1446.12 955.833,1446.05 956.789,1446.07 957.744,1446.04 \n",
       "  958.7,1446.02 959.655,1446.02 960.611,1446.05 961.566,1446.12 962.522,1446.07 963.477,1446.11 964.433,1446.18 965.388,1446.13 966.344,1446.07 967.299,1446.06 \n",
       "  968.255,1446.11 969.21,1446.11 970.166,1446.08 971.121,1446.06 972.077,1446.09 973.032,1446.12 973.988,1446.19 974.943,1446.18 975.899,1446.14 976.854,1446.16 \n",
       "  977.81,1446.18 978.765,1446.16 979.721,1446.15 980.676,1446.15 981.632,1446.08 982.587,1445.94 983.543,1446.01 984.499,1446.05 985.454,1446 986.41,1445.96 \n",
       "  987.365,1445.91 988.321,1445.94 989.276,1445.98 990.232,1446.03 991.187,1446.01 992.143,1445.98 993.098,1445.9 994.054,1445.94 995.009,1445.89 995.965,1445.88 \n",
       "  996.92,1445.95 997.876,1445.83 998.831,1445.85 999.787,1445.91 1000.74,1445.86 1001.7,1445.81 1002.65,1445.82 1003.61,1445.85 1004.56,1445.79 1005.52,1445.81 \n",
       "  1006.48,1445.74 1007.43,1445.78 1008.39,1445.74 1009.34,1445.7 1010.3,1445.43 1011.25,1445.47 1012.21,1445.45 1013.16,1445.44 1014.12,1445.48 1015.07,1445.52 \n",
       "  1016.03,1445.52 1016.99,1445.51 1017.94,1445.44 1018.9,1445.41 1019.85,1445.36 1020.81,1445.34 1021.76,1445.3 1022.72,1445.29 1023.67,1445.31 1024.63,1445.28 \n",
       "  1025.59,1445.28 1026.54,1445.29 1027.5,1445.38 1028.45,1445.34 1029.41,1445.28 1030.36,1445.28 1031.32,1445.33 1032.27,1445.39 1033.23,1445.36 1034.18,1445.36 \n",
       "  1035.14,1445.38 1036.1,1445.32 1037.05,1445.38 1038.01,1445.45 1038.96,1445.42 1039.92,1445.51 1040.87,1445.57 1041.83,1445.54 1042.78,1445.47 1043.74,1445.41 \n",
       "  1044.7,1445.4 1045.65,1445.33 1046.61,1445.33 1047.56,1445.39 1048.52,1445.45 1049.47,1445.4 1050.43,1445.4 1051.38,1445.39 1052.34,1445.4 1053.3,1445.53 \n",
       "  1054.25,1445.53 1055.21,1445.56 1056.16,1445.51 1057.12,1445.46 1058.07,1445.5 1059.03,1445.41 1059.98,1445.48 1060.94,1445.45 1061.89,1445.54 1062.85,1445.63 \n",
       "  1063.81,1445.59 1064.76,1445.55 1065.72,1445.51 1066.67,1445.47 1067.63,1445.54 1068.58,1445.5 1069.54,1445.46 1070.49,1445.47 1071.45,1445.47 1072.41,1445.3 \n",
       "  1073.36,1445.34 1074.32,1445.35 1075.27,1445.38 1076.23,1445.4 1077.18,1445.4 1078.14,1445.37 1079.09,1445.36 1080.05,1445.4 1081,1445.39 1081.96,1445.38 \n",
       "  1082.92,1445.38 1083.87,1445.27 1084.83,1445.29 1085.78,1445.3 1086.74,1445.31 1087.69,1445.39 1088.65,1445.54 1089.6,1445.59 1090.56,1445.57 1091.52,1445.6 \n",
       "  1092.47,1445.58 1093.43,1445.52 1094.38,1445.47 1095.34,1445.56 1096.29,1445.51 1097.25,1445.51 1098.2,1445.47 1099.16,1445.53 1100.11,1445.53 1101.07,1445.52 \n",
       "  1102.03,1445.51 1102.98,1445.51 1103.94,1445.49 1104.89,1445.49 1105.85,1445.42 1106.8,1445.43 1107.76,1445.38 1108.71,1445.37 1109.67,1445.41 1110.63,1445.38 \n",
       "  1111.58,1445.42 1112.54,1445.39 1113.49,1445.42 1114.45,1445.55 1115.4,1445.55 1116.36,1445.51 1117.31,1445.46 1118.27,1445.47 1119.23,1445.47 1120.18,1445.44 \n",
       "  1121.14,1445.4 1122.09,1445.42 1123.05,1445.51 1124,1445.56 1124.96,1445.56 1125.91,1445.52 1126.87,1445.48 1127.82,1445.5 1128.78,1445.5 1129.74,1445.5 \n",
       "  1130.69,1445.51 1131.65,1445.51 1132.6,1445.54 1133.56,1445.59 1134.51,1445.64 1135.47,1445.69 1136.42,1445.7 1137.38,1445.69 1138.34,1445.73 1139.29,1445.74 \n",
       "  1140.25,1445.69 1141.2,1445.57 1142.16,1445.63 1143.11,1445.64 1144.07,1445.6 1145.02,1445.52 1145.98,1445.58 1146.93,1445.6 1147.89,1445.59 1148.85,1445.62 \n",
       "  1149.8,1445.56 1150.76,1445.6 1151.71,1445.58 1152.67,1445.64 1153.62,1445.69 1154.58,1445.67 1155.53,1445.71 1156.49,1445.73 1157.45,1445.71 1158.4,1445.7 \n",
       "  1159.36,1445.71 1160.31,1445.68 1161.27,1445.64 1162.22,1445.64 1163.18,1445.68 1164.13,1445.72 1165.09,1445.71 1166.04,1445.69 1167,1445.69 1167.96,1445.63 \n",
       "  1168.91,1445.62 1169.87,1445.58 1170.82,1445.59 1171.78,1445.53 1172.73,1445.59 1173.69,1445.58 1174.64,1445.52 1175.6,1445.53 1176.56,1445.53 1177.51,1445.55 \n",
       "  1178.47,1445.58 1179.42,1445.58 1180.38,1445.58 1181.33,1445.5 1182.29,1445.43 1183.24,1445.37 1184.2,1445.36 1185.15,1445.39 1186.11,1445.37 1187.07,1445.38 \n",
       "  1188.02,1445.34 1188.98,1445.42 1189.93,1445.39 1190.89,1445.39 1191.84,1445.37 1192.8,1445.32 1193.75,1445.34 1194.71,1445.33 1195.67,1445.36 1196.62,1445.4 \n",
       "  1197.58,1445.38 1198.53,1445.38 1199.49,1445.39 1200.44,1445.37 1201.4,1445.39 1202.35,1445.4 1203.31,1445.4 1204.27,1445.37 1205.22,1445.36 1206.18,1445.34 \n",
       "  1207.13,1445.34 1208.09,1445.27 1209.04,1445.21 1210,1445.22 1210.95,1445.18 1211.91,1445.16 1212.86,1445.11 1213.82,1445.04 1214.78,1445.03 1215.73,1445.06 \n",
       "  1216.69,1445.03 1217.64,1445.01 1218.6,1444.99 1219.55,1445.01 1220.51,1445.01 1221.46,1445.18 1222.42,1445.15 1223.38,1445.16 1224.33,1445.17 1225.29,1445.18 \n",
       "  1226.24,1445.16 1227.2,1445.2 1228.15,1445.18 1229.11,1445.09 1230.06,1445.09 1231.02,1445.05 1231.97,1445.08 1232.93,1445.04 1233.89,1445.04 1234.84,1445.14 \n",
       "  1235.8,1445.13 1236.75,1445.13 1237.71,1445.13 1238.66,1445.12 1239.62,1445.1 1240.57,1445 1241.53,1444.94 1242.49,1445 1243.44,1444.99 1244.4,1445.01 \n",
       "  1245.35,1445 1246.31,1444.95 1247.26,1445.11 1248.22,1445.11 1249.17,1445.01 1250.13,1444.88 1251.08,1444.92 1252.04,1444.93 1253,1444.8 1253.95,1444.65 \n",
       "  1254.91,1444.7 1255.86,1444.67 1256.82,1444.63 1257.77,1444.67 1258.73,1444.68 1259.68,1444.68 1260.64,1444.67 1261.6,1444.65 1262.55,1444.58 1263.51,1444.66 \n",
       "  1264.46,1444.62 1265.42,1444.63 1266.37,1444.65 1267.33,1444.52 1268.28,1444.55 1269.24,1444.48 1270.2,1444.5 1271.15,1444.56 1272.11,1444.59 1273.06,1444.73 \n",
       "  1274.02,1444.76 1274.97,1444.68 1275.93,1444.82 1276.88,1444.82 1277.84,1444.8 1278.79,1444.75 1279.75,1444.77 1280.71,1444.76 1281.66,1444.8 1282.62,1444.76 \n",
       "  1283.57,1444.74 1284.53,1444.77 1285.48,1444.76 1286.44,1444.8 1287.39,1444.83 1288.35,1444.9 1289.31,1444.89 1290.26,1444.94 1291.22,1445.02 1292.17,1445 \n",
       "  1293.13,1445.08 1294.08,1445.03 1295.04,1445.06 1295.99,1445.01 1296.95,1445 1297.9,1445.08 1298.86,1445.12 1299.82,1445.16 1300.77,1445.09 1301.73,1445.1 \n",
       "  1302.68,1445.07 1303.64,1445.1 1304.59,1445.04 1305.55,1445.06 1306.5,1444.95 1307.46,1444.9 1308.42,1444.81 1309.37,1444.8 1310.33,1444.78 1311.28,1444.93 \n",
       "  1312.24,1444.93 1313.19,1444.87 1314.15,1444.94 1315.1,1444.96 1316.06,1445.04 1317.01,1444.97 1317.97,1444.95 1318.93,1444.93 1319.88,1444.95 1320.84,1444.96 \n",
       "  1321.79,1444.88 1322.75,1444.95 1323.7,1445 1324.66,1444.98 1325.61,1445.01 1326.57,1445.04 1327.53,1445.03 1328.48,1445 1329.44,1444.96 1330.39,1444.97 \n",
       "  1331.35,1444.94 1332.3,1444.86 1333.26,1444.87 1334.21,1444.8 1335.17,1444.81 1336.13,1444.73 1337.08,1444.72 1338.04,1444.68 1338.99,1444.78 1339.95,1444.81 \n",
       "  1340.9,1444.84 1341.86,1444.82 1342.81,1444.77 1343.77,1444.77 1344.72,1444.79 1345.68,1444.75 1346.64,1444.7 1347.59,1444.69 1348.55,1444.71 1349.5,1444.82 \n",
       "  1350.46,1444.84 1351.41,1445 1352.37,1444.86 1353.32,1444.78 1354.28,1444.61 1355.24,1444.87 1356.19,1444.87 1357.15,1444.86 1358.1,1444.87 1359.06,1444.79 \n",
       "  1360.01,1444.82 1360.97,1444.75 1361.92,1444.8 1362.88,1444.78 1363.83,1444.76 1364.79,1444.83 1365.75,1444.85 1366.7,1444.84 1367.66,1444.77 1368.61,1444.72 \n",
       "  1369.57,1444.79 1370.52,1444.76 1371.48,1444.77 1372.43,1444.78 1373.39,1444.81 1374.35,1444.76 1375.3,1444.82 1376.26,1444.66 1377.21,1444.72 1378.17,1444.67 \n",
       "  1379.12,1444.77 1380.08,1444.78 1381.03,1444.8 1381.99,1444.73 1382.94,1444.7 1383.9,1444.6 1384.86,1444.57 1385.81,1444.6 1386.77,1444.59 1387.72,1444.52 \n",
       "  1388.68,1444.39 1389.63,1444.3 1390.59,1444.29 1391.54,1444.35 1392.5,1444.39 1393.46,1444.33 1394.41,1444.24 1395.37,1444.34 1396.32,1444.3 1397.28,1444.52 \n",
       "  1398.23,1444.66 1399.19,1444.7 1400.14,1444.69 1401.1,1444.73 1402.06,1444.7 1403.01,1444.79 1403.97,1444.86 1404.92,1444.79 1405.88,1444.89 1406.83,1444.87 \n",
       "  1407.79,1444.84 1408.74,1444.89 1409.7,1444.82 1410.65,1444.82 1411.61,1444.82 1412.57,1444.82 1413.52,1444.84 1414.48,1444.78 1415.43,1444.82 1416.39,1444.81 \n",
       "  1417.34,1444.83 1418.3,1444.78 1419.25,1444.83 1420.21,1444.75 1421.17,1444.88 1422.12,1444.85 1423.08,1444.92 1424.03,1444.88 1424.99,1444.87 1425.94,1444.81 \n",
       "  1426.9,1444.82 1427.85,1444.82 1428.81,1444.78 1429.76,1444.7 1430.72,1444.73 1431.68,1444.75 1432.63,1444.76 1433.59,1444.81 1434.54,1444.76 1435.5,1444.84 \n",
       "  1436.45,1444.85 1437.41,1444.81 1438.36,1444.74 1439.32,1444.78 1440.28,1444.89 1441.23,1444.96 1442.19,1445.04 1443.14,1445.09 1444.1,1445.03 1445.05,1444.95 \n",
       "  1446.01,1444.9 1446.96,1444.99 1447.92,1445.12 1448.87,1445.02 1449.83,1445.03 1450.79,1445.05 1451.74,1445.01 1452.7,1444.99 1453.65,1445.06 1454.61,1445.02 \n",
       "  1455.56,1444.98 1456.52,1445.02 1457.47,1445.08 1458.43,1445.03 1459.39,1445 1460.34,1444.98 1461.3,1445.03 1462.25,1444.84 1463.21,1444.91 1464.16,1444.88 \n",
       "  1465.12,1444.94 1466.07,1445.02 1467.03,1445.02 1467.99,1444.99 1468.94,1445.07 1469.9,1445.09 1470.85,1444.92 1471.81,1444.95 1472.76,1445 1473.72,1445.11 \n",
       "  1474.67,1445.08 1475.63,1444.82 1476.58,1444.76 1477.54,1444.58 1478.5,1444.55 1479.45,1444.43 1480.41,1444.52 1481.36,1444.46 1482.32,1444.42 1483.27,1444.45 \n",
       "  1484.23,1444.45 1485.18,1444.45 1486.14,1444.44 1487.1,1444.41 1488.05,1444.52 1489.01,1444.49 1489.96,1444.38 1490.92,1444.45 1491.87,1444.51 1492.83,1444.49 \n",
       "  1493.78,1444.57 1494.74,1444.58 1495.69,1444.58 1496.65,1444.58 1497.61,1444.54 1498.56,1444.51 1499.52,1444.5 1500.47,1444.52 1501.43,1444.44 1502.38,1444.38 \n",
       "  1503.34,1444.39 1504.29,1444.41 1505.25,1444.39 1506.21,1444.44 1507.16,1444.48 1508.12,1444.47 1509.07,1444.43 1510.03,1444.35 1510.98,1444.4 1511.94,1444.43 \n",
       "  1512.89,1444.53 1513.85,1444.45 1514.8,1444.56 1515.76,1444.53 1516.72,1444.37 1517.67,1444.51 1518.63,1444.3 1519.58,1444.2 1520.54,1444.13 1521.49,1444.09 \n",
       "  1522.45,1444.28 1523.4,1444.24 1524.36,1444.18 1525.32,1444.18 1526.27,1444.12 1527.23,1444.05 1528.18,1444.01 1529.14,1443.92 1530.09,1444.03 1531.05,1443.98 \n",
       "  1532,1443.86 1532.96,1443.76 1533.92,1443.92 1534.87,1443.83 1535.83,1443.54 1536.78,1443.74 1537.74,1443.83 1538.69,1443.93 1539.65,1443.76 1540.6,1443.57 \n",
       "  1541.56,1443.4 1542.51,1443.32 1543.47,1443.31 1544.43,1443.7 1545.38,1443.8 1546.34,1444.03 1547.29,1444.02 1548.25,1443.97 1549.2,1443.92 1550.16,1443.78 \n",
       "  1551.11,1443.7 1552.07,1443.56 1553.03,1443.44 1553.98,1443.39 1554.94,1443.2 1555.89,1443.41 1556.85,1443.27 1557.8,1443.28 1558.76,1443.17 1559.71,1443.17 \n",
       "  1560.67,1443.18 1561.62,1443.4 1562.58,1443.52 1563.54,1443.62 1564.49,1443.75 1565.45,1443.76 1566.4,1443.56 1567.36,1443.65 1568.31,1443.74 1569.27,1443.88 \n",
       "  1570.22,1444 1571.18,1444.03 1572.14,1443.82 1573.09,1443.73 1574.05,1443.67 1575,1443.76 1575.96,1443.69 1576.91,1443.77 1577.87,1443.92 1578.82,1444.05 \n",
       "  1579.78,1444.05 1580.73,1443.9 1581.69,1443.83 1582.65,1443.82 1583.6,1443.88 1584.56,1443.84 1585.51,1443.87 1586.47,1443.95 1587.42,1444.02 1588.38,1444 \n",
       "  1589.33,1443.9 1590.29,1443.87 1591.25,1443.88 1592.2,1443.85 1593.16,1443.95 1594.11,1443.97 1595.07,1443.84 1596.02,1444.06 1596.98,1444.16 1597.93,1444.23 \n",
       "  1598.89,1444.13 1599.85,1444.36 1600.8,1444.24 1601.76,1444.19 1602.71,1444.06 1603.67,1444.16 1604.62,1444.11 1605.58,1444.14 1606.53,1444.19 1607.49,1444.35 \n",
       "  1608.44,1444.24 1609.4,1444.32 1610.36,1444.22 1611.31,1444.04 1612.27,1444 1613.22,1443.87 1614.18,1444.08 1615.13,1444.05 1616.09,1444.02 1617.04,1444.12 \n",
       "  1618,1444.23 1618.96,1444.27 1619.91,1444.12 1620.87,1444.12 1621.82,1443.96 1622.78,1443.85 1623.73,1444.11 1624.69,1444.01 1625.64,1443.99 1626.6,1444.07 \n",
       "  1627.55,1444.05 1628.51,1444.03 1629.47,1443.72 1630.42,1443.69 1631.38,1443.7 1632.33,1443.78 1633.29,1443.89 1634.24,1443.81 1635.2,1443.91 1636.15,1443.81 \n",
       "  1637.11,1443.94 1638.07,1443.97 1639.02,1444.03 1639.98,1443.93 1640.93,1443.91 1641.89,1444.02 1642.84,1443.99 1643.8,1444.05 1644.75,1443.9 1645.71,1443.91 \n",
       "  1646.66,1444.13 1647.62,1444.15 1648.58,1444.11 1649.53,1444.05 1650.49,1444.19 1651.44,1444.04 1652.4,1443.88 1653.35,1443.74 1654.31,1443.88 1655.26,1443.91 \n",
       "  1656.22,1444 1657.18,1444.02 1658.13,1443.95 1659.09,1444.19 1660.04,1444.2 1661,1444.15 1661.95,1444.15 1662.91,1444.27 1663.86,1444.12 1664.82,1444.11 \n",
       "  1665.78,1444.04 1666.73,1444.05 1667.69,1444.01 1668.64,1443.86 1669.6,1443.67 1670.55,1443.71 1671.51,1443.69 1672.46,1443.65 1673.42,1443.61 1674.37,1443.62 \n",
       "  1675.33,1443.66 1676.29,1443.69 1677.24,1443.77 1678.2,1443.76 1679.15,1443.83 1680.11,1443.89 1681.06,1444 1682.02,1444 1682.97,1444.02 1683.93,1444.19 \n",
       "  1684.89,1444.19 1685.84,1444.1 1686.8,1444.13 1687.75,1444.07 1688.71,1444.05 1689.66,1444.03 1690.62,1444.05 1691.57,1443.95 1692.53,1443.79 1693.48,1443.77 \n",
       "  1694.44,1443.75 1695.4,1443.73 1696.35,1443.76 1697.31,1443.82 1698.26,1443.8 1699.22,1443.8 1700.17,1443.74 1701.13,1443.69 1702.08,1443.7 1703.04,1443.64 \n",
       "  1704,1443.63 1704.95,1443.52 1705.91,1443.51 1706.86,1443.43 1707.82,1443.57 1708.77,1443.46 1709.73,1443.53 1710.68,1443.55 1711.64,1443.51 1712.59,1443.49 \n",
       "  1713.55,1443.48 1714.51,1443.49 1715.46,1443.49 1716.42,1443.45 1717.37,1443.54 1718.33,1443.48 1719.28,1443.63 1720.24,1443.47 1721.19,1443.55 1722.15,1443.47 \n",
       "  1723.11,1443.46 1724.06,1443.51 1725.02,1443.59 1725.97,1443.55 1726.93,1443.5 1727.88,1443.53 1728.84,1443.46 1729.79,1443.44 1730.75,1443.59 1731.71,1443.56 \n",
       "  1732.66,1443.55 1733.62,1443.59 1734.57,1443.53 1735.53,1443.46 1736.48,1443.4 1737.44,1443.39 1738.39,1443.46 1739.35,1443.47 1740.3,1443.42 1741.26,1443.4 \n",
       "  1742.22,1443.37 1743.17,1443.42 1744.13,1443.48 1745.08,1443.39 1746.04,1443.33 1746.99,1443.33 1747.95,1443.29 1748.9,1443.39 1749.86,1443.42 1750.82,1443.53 \n",
       "  1751.77,1443.56 1752.73,1443.54 1753.68,1443.56 1754.64,1443.58 1755.59,1443.53 1756.55,1443.58 1757.5,1443.59 1758.46,1443.63 1759.41,1443.63 1760.37,1443.6 \n",
       "  1761.33,1443.57 1762.28,1443.58 1763.24,1443.63 1764.19,1443.62 1765.15,1443.67 1766.1,1443.82 1767.06,1443.72 1768.01,1443.71 1768.97,1443.73 1769.93,1443.74 \n",
       "  1770.88,1443.73 1771.84,1443.66 1772.79,1443.6 1773.75,1443.56 1774.7,1443.56 1775.66,1443.54 1776.61,1443.57 1777.57,1443.63 1778.52,1443.68 1779.48,1443.63 \n",
       "  1780.44,1443.61 1781.39,1443.61 1782.35,1443.47 1783.3,1443.5 1784.26,1443.49 1785.21,1443.54 1786.17,1443.61 1787.12,1443.57 1788.08,1443.61 1789.04,1443.64 \n",
       "  1789.99,1443.61 1790.95,1443.72 1791.9,1443.78 1792.86,1443.8 1793.81,1443.79 1794.77,1443.78 1795.72,1443.8 1796.68,1443.84 1797.63,1443.9 1798.59,1443.84 \n",
       "  1799.55,1443.78 1800.5,1443.8 1801.46,1443.82 1802.41,1443.85 1803.37,1443.87 1804.32,1443.94 1805.28,1443.92 1806.23,1443.91 1807.19,1443.87 1808.15,1443.89 \n",
       "  1809.1,1443.77 1810.06,1443.71 1811.01,1443.75 1811.97,1443.77 1812.92,1443.71 1813.88,1443.81 1814.83,1443.83 1815.79,1443.85 1816.75,1443.87 1817.7,1443.88 \n",
       "  1818.66,1443.85 1819.61,1443.9 1820.57,1443.88 1821.52,1443.92 1822.48,1443.93 1823.43,1443.91 1824.39,1443.89 1825.34,1443.88 1826.3,1443.88 1827.26,1443.85 \n",
       "  1828.21,1443.75 1829.17,1443.77 1830.12,1443.72 1831.08,1443.73 1832.03,1443.66 1832.99,1443.63 1833.94,1443.66 1834.9,1443.66 1835.86,1443.54 1836.81,1443.56 \n",
       "  1837.77,1443.56 1838.72,1443.5 1839.68,1443.56 1840.63,1443.57 1841.59,1443.55 1842.54,1443.57 1843.5,1443.51 1844.45,1443.36 1845.41,1443.38 1846.37,1443.41 \n",
       "  1847.32,1443.42 1848.28,1443.39 1849.23,1443.32 1850.19,1443.26 1851.14,1443.26 1852.1,1443.32 1853.05,1443.33 1854.01,1443.34 1854.97,1443.35 1855.92,1443.38 \n",
       "  1856.88,1443.4 1857.83,1443.36 1858.79,1443.34 1859.74,1443.28 1860.7,1443.29 1861.65,1443.28 1862.61,1443.25 1863.56,1443.26 1864.52,1443.24 1865.48,1443.32 \n",
       "  1866.43,1443.3 1867.39,1443.34 1868.34,1443.33 1869.3,1443.3 1870.25,1443.28 1871.21,1443.31 1872.16,1443.34 1873.12,1443.35 1874.08,1443.38 1875.03,1443.36 \n",
       "  1875.99,1443.35 1876.94,1443.47 1877.9,1443.48 1878.85,1443.49 1879.81,1443.47 1880.76,1443.4 1881.72,1443.41 1882.68,1443.42 1883.63,1443.41 1884.59,1443.37 \n",
       "  1885.54,1443.38 1886.5,1443.42 1887.45,1443.44 1888.41,1443.43 1889.36,1443.4 1890.32,1443.41 1891.27,1443.42 1892.23,1443.4 1893.19,1443.39 1894.14,1443.32 \n",
       "  1895.1,1443.23 1896.05,1443.25 1897.01,1443.28 1897.96,1443.27 1898.92,1443.27 1899.87,1443.29 1900.83,1443.25 1901.79,1443.24 1902.74,1443.18 1903.7,1443.19 \n",
       "  1904.65,1443.21 1905.61,1443.17 1906.56,1443.23 1907.52,1443.24 1908.47,1443.22 1909.43,1443.15 1910.38,1443.14 1911.34,1443.23 1912.3,1443.24 1913.25,1443.26 \n",
       "  1914.21,1443.26 1915.16,1443.22 1916.12,1443.26 1917.07,1443.25 1918.03,1443.22 1918.98,1443.2 1919.94,1443.24 1920.9,1443.24 1921.85,1443.25 1922.81,1443.24 \n",
       "  1923.76,1443.3 1924.72,1443.34 1925.67,1443.32 1926.63,1443.43 1927.58,1443.42 1928.54,1443.33 1929.49,1443.33 1930.45,1443.39 1931.41,1443.45 1932.36,1443.5 \n",
       "  1933.32,1443.48 1934.27,1443.48 1935.23,1443.54 1936.18,1443.51 1937.14,1443.54 1938.09,1443.52 1939.05,1443.53 1940.01,1443.5 1940.96,1443.53 1941.92,1443.44 \n",
       "  1942.87,1443.47 1943.83,1443.43 1944.78,1443.34 1945.74,1443.28 1946.69,1443.32 1947.65,1443.34 1948.61,1443.22 1949.56,1443.21 1950.52,1443.34 1951.47,1443.33 \n",
       "  1952.43,1443.3 1953.38,1443.32 1954.34,1443.28 1955.29,1443.28 1956.25,1443.31 1957.2,1443.33 1958.16,1443.34 1959.12,1443.33 1960.07,1443.4 1961.03,1443.49 \n",
       "  1961.98,1443.46 1962.94,1443.52 1963.89,1443.5 1964.85,1443.51 1965.8,1443.55 1966.76,1443.49 1967.72,1443.47 1968.67,1443.52 1969.63,1443.51 1970.58,1443.51 \n",
       "  1971.54,1443.54 1972.49,1443.63 1973.45,1443.56 1974.4,1443.66 1975.36,1443.58 1976.31,1443.54 1977.27,1443.6 1978.23,1443.58 1979.18,1443.56 1980.14,1443.6 \n",
       "  1981.09,1443.59 1982.05,1443.59 1983,1443.66 1983.96,1443.7 1984.91,1443.73 1985.87,1443.76 1986.83,1443.78 1987.78,1443.85 1988.74,1443.92 1989.69,1443.93 \n",
       "  1990.65,1443.99 1991.6,1444 1992.56,1444.01 1993.51,1444.01 1994.47,1443.95 1995.42,1443.97 1996.38,1444.02 1997.34,1443.98 1998.29,1444.01 1999.25,1444.06 \n",
       "  2000.2,1444.06 2001.16,1444.06 2002.11,1444.08 2003.07,1444.13 2004.02,1444.16 2004.98,1444.21 2005.94,1444.2 2006.89,1444.2 2007.85,1444.17 2008.8,1444.18 \n",
       "  2009.76,1444.18 2010.71,1444.15 2011.67,1444.12 2012.62,1444.13 2013.58,1444.13 2014.54,1444.12 2015.49,1444.15 2016.45,1444.19 2017.4,1444.22 2018.36,1444.17 \n",
       "  2019.31,1444.18 2020.27,1444.18 2021.22,1444.22 2022.18,1444.24 2023.13,1444.25 2024.09,1444.22 2025.05,1444.23 2026,1444.29 2026.96,1444.36 2027.91,1444.34 \n",
       "  2028.87,1444.37 2029.82,1444.32 2030.78,1444.4 2031.73,1444.43 2032.69,1444.36 2033.65,1444.34 2034.6,1444.33 2035.56,1444.57 2036.51,1444.55 2037.47,1444.58 \n",
       "  2038.42,1444.56 2039.38,1444.66 2040.33,1444.7 2041.29,1444.81 2042.24,1444.84 2043.2,1444.85 2044.16,1444.91 2045.11,1444.86 2046.07,1444.81 2047.02,1444.87 \n",
       "  2047.98,1444.94 2048.93,1444.98 2049.89,1444.94 2050.84,1444.92 2051.8,1444.96 2052.76,1444.93 2053.71,1444.91 2054.67,1444.92 2055.62,1444.95 2056.58,1444.95 \n",
       "  2057.53,1444.94 2058.49,1444.95 2059.44,1444.96 2060.4,1444.95 2061.35,1445.01 2062.31,1444.88 2063.27,1444.85 2064.22,1444.78 2065.18,1444.78 2066.13,1444.77 \n",
       "  2067.09,1444.78 2068.04,1444.75 2069,1444.77 2069.95,1444.69 2070.91,1444.7 2071.87,1444.65 2072.82,1444.65 2073.78,1444.66 2074.73,1444.58 2075.69,1444.53 \n",
       "  2076.64,1444.54 2077.6,1444.6 2078.55,1444.62 2079.51,1444.63 2080.47,1444.58 2081.42,1444.6 2082.38,1444.58 2083.33,1444.56 2084.29,1444.56 2085.24,1444.59 \n",
       "  2086.2,1444.51 2087.15,1444.51 2088.11,1444.56 2089.06,1444.48 2090.02,1444.52 2090.98,1444.58 2091.93,1444.56 2092.89,1444.62 2093.84,1444.64 2094.8,1444.87 \n",
       "  2095.75,1444.87 2096.71,1444.84 2097.66,1444.85 2098.62,1444.85 2099.58,1444.83 2100.53,1444.9 2101.49,1444.81 2102.44,1444.77 2103.4,1444.79 2104.35,1444.83 \n",
       "  2105.31,1444.9 2106.26,1444.84 2107.22,1444.81 2108.17,1444.88 2109.13,1444.89 2110.09,1444.88 2111.04,1444.9 2112,1444.9 2112.95,1445.01 2113.91,1444.89 \n",
       "  2114.86,1444.83 2115.82,1444.88 2116.77,1444.8 2117.73,1444.88 2118.69,1444.7 2119.64,1444.7 2120.6,1444.65 2121.55,1444.72 2122.51,1444.82 2123.46,1444.8 \n",
       "  2124.42,1444.78 2125.37,1444.82 2126.33,1444.87 2127.28,1444.87 2128.24,1444.94 2129.2,1444.92 2130.15,1444.89 2131.11,1444.84 2132.06,1444.87 2133.02,1444.86 \n",
       "  2133.97,1444.86 2134.93,1444.87 2135.88,1444.92 2136.84,1444.97 2137.8,1445 2138.75,1445.02 2139.71,1445.03 2140.66,1445.02 2141.62,1445.07 2142.57,1444.98 \n",
       "  2143.53,1444.92 2144.48,1444.96 2145.44,1444.93 2146.4,1444.88 2147.35,1444.91 2148.31,1444.86 2149.26,1444.84 2150.22,1444.81 2151.17,1444.83 2152.13,1444.88 \n",
       "  2153.08,1444.9 2154.04,1444.82 2154.99,1444.97 2155.95,1445.03 2156.91,1444.96 2157.86,1444.96 2158.82,1445 2159.77,1445.08 2160.73,1445.07 2161.68,1445.04 \n",
       "  2162.64,1445.05 2163.59,1445 2164.55,1445.04 2165.51,1445.08 2166.46,1445.06 2167.42,1445.02 2168.37,1444.97 2169.33,1444.93 2170.28,1444.92 2171.24,1445.02 \n",
       "  2172.19,1445.02 2173.15,1445 2174.1,1444.95 2175.06,1444.94 2176.02,1445.01 2176.97,1444.96 2177.93,1444.93 2178.88,1444.98 2179.84,1445.04 2180.79,1445.06 \n",
       "  2181.75,1445.03 2182.7,1445.01 2183.66,1445.04 2184.62,1445.02 2185.57,1445.24 2186.53,1445.24 2187.48,1445.24 2188.44,1445.29 2189.39,1445.33 2190.35,1445.35 \n",
       "  2191.3,1445.3 2192.26,1445.31 2193.21,1445.28 2194.17,1445.25 2195.13,1445.25 2196.08,1445.24 2197.04,1445.21 2197.99,1445.2 2198.95,1445.28 2199.9,1445.25 \n",
       "  2200.86,1445.22 2201.81,1445.21 2202.77,1445.17 2203.73,1445.24 2204.68,1445.21 2205.64,1445.21 2206.59,1445.2 2207.55,1445.18 2208.5,1445.06 2209.46,1445.16 \n",
       "  2210.41,1445.06 2211.37,1445.17 2212.33,1445.06 2213.28,1445.16 2214.24,1445.03 2215.19,1444.99 2216.15,1445.03 2217.1,1445.07 2218.06,1445.09 2219.01,1445.14 \n",
       "  2219.97,1445.04 2220.92,1444.97 2221.88,1445.05 2222.84,1445.24 2223.79,1445.27 2224.75,1445.11 2225.7,1445.18 2226.66,1445.16 2227.61,1445.19 2228.57,1445.19 \n",
       "  2229.52,1445.21 2230.48,1445.21 2231.44,1445.22 2232.39,1445.27 2233.35,1445.23 2234.3,1445.12 2235.26,1445.1 2236.21,1445.16 2237.17,1445.21 2238.12,1445.19 \n",
       "  2239.08,1445.27 2240.03,1445.34 2240.99,1445.31 2241.95,1445.32 2242.9,1445.29 2243.86,1445.29 2244.81,1445.29 2245.77,1445.35 2246.72,1445.34 2247.68,1445.27 \n",
       "  2248.63,1445.24 2249.59,1445.22 2250.55,1445.22 2251.5,1445.22 2252.46,1445.11 2253.41,1445.12 2254.37,1445.19 2255.32,1445.15 2256.28,1445.15 2257.23,1445.2 \n",
       "  2258.19,1445.26 2259.14,1445.25 2260.1,1445.21 2261.06,1445.14 2262.01,1445.13 2262.97,1445.22 2263.92,1445.17 2264.88,1445.09 2265.83,1445.12 2266.79,1445.11 \n",
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     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rho = 0.20/250; # 20%\n",
    "w = port_opt(R,rho);\n",
    "r = R*w; # Portfolio return time series\n",
    "pf_return = 250*avg(r)\n",
    "plot!(1:T, cum_value(r), label= \"20%\")\n",
    "\n",
    "rho = 0.40/250; # 40%\n",
    "w = port_opt(R,rho);\n",
    "r = R*w; # Portfolio return time series\n",
    "pf_return = 250*avg(r)\n",
    "plot!(1:T, cum_value(r), label= \"40%\")\n",
    "\n",
    "rho = (1/length(R))/250; # 1/n\n",
    "w = port_opt(R,rho);\n",
    "r = R*w; # Portfolio return time series\n",
    "pf_return = 250*avg(r)\n",
    "plot!(1:T, cum_value(r), label= \"1/n\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Figure 17.2** <a ind=\"#fig2\"></a>Total value over time for four portfolios: the Pareto optimal portfolios with $10%, 20%$, and $40%$ return, and the uniform portfolio. The total value is computed using the $2000 × 20$ daily return matrix $R$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 17.2 Linear quadratic control\n",
    "We implement linear quadratic control, as described in VMLS §[17.2](https://web.stanford.edu/~boyd/vmls/vmls.pdf#section.17.2), for a time- invariant system with matrices $A, B$, and $C$.\n",
    "\n",
    "**Kronecker product.** To create the big matrices $Ã$ and $C̃$, we need to define block diagonal matrices with the same matrix repeated a number of times along the diagonal. There are many ways to do this in Julia. One of the simplest ways uses the `kron` function, for the Kronecker product of two matrices. The Kronecker product of an $m × n$ matrix $G$ and a $p × q$ matrix $H$ is defined as the $mp × nq$ block matrix \n",
    "$$\n",
    "\\begin{bmatrix}\n",
    "G_{11}H &  G_{12}H &  \\dots  & G_{1n}H \\\\\n",
    "G_{21}H &  G_{22}H &  \\dots  & G_{2n}H \\\\\n",
    "\\vdots & \\vdots & \\ddots & \\vdots \\\\\n",
    "G_{m1}H &  G_{m2}H &  \\dots  & G_{mn}H\n",
    "\\end{bmatrix} . \n",
    "$$\n",
    "It is computed in Julia as `kron(G,H)`. If $G$ is an $n × n$ identity matrix, we obtain the block diagonal matrix with $H$ repeated $n$ times on the diagonal."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2×2 Array{Float64,2}:\n",
       " -0.465825   0.318543\n",
       "  1.42805   -1.58887 "
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "H = randn(2,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6×6 Array{Float64,2}:\n",
       " -0.465825   0.318543  -0.0        0.0       -0.0        0.0     \n",
       "  1.42805   -1.58887    0.0       -0.0        0.0       -0.0     \n",
       " -0.0        0.0       -0.465825   0.318543  -0.0        0.0     \n",
       "  0.0       -0.0        1.42805   -1.58887    0.0       -0.0     \n",
       " -0.0        0.0       -0.0        0.0       -0.465825   0.318543\n",
       "  0.0       -0.0        0.0       -0.0        1.42805   -1.58887 "
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kron(eye(3),H)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "An alternative method uses the Julia `cat` function for constructing block matrices:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6×6 Array{Float64,2}:\n",
       " -0.465825   0.318543   0.0        0.0        0.0        0.0     \n",
       "  1.42805   -1.58887    0.0        0.0        0.0        0.0     \n",
       "  0.0        0.0       -0.465825   0.318543   0.0        0.0     \n",
       "  0.0        0.0        1.42805   -1.58887    0.0        0.0     \n",
       "  0.0        0.0        0.0        0.0       -0.465825   0.318543\n",
       "  0.0        0.0        0.0        0.0        1.42805   -1.58887 "
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cat([H for k=1:3]..., dims=(1,2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Linear quadratic control example.** We start by writing a function `lqr` that con- structs and solves the constrained least squares problem for linear quadratic control. The function returns three arrays\n",
    "```Julia\n",
    "x = [ x[1], x[2], ..., x[T] ],\n",
    "u = [ u[1], u[2], ..., u[T-1] ],\n",
    "y = [ y[1], y[2], ..., y[T] ]. \n",
    "```\n",
    "The first two contain the optimal solution of the problem. The third array contains\n",
    "$y_t = Cx_t$. \n",
    "\n",
    "We allow the input arguments `x_init` and `x_des` to be matrices, so we can solve the same problem for different pairs of initial and end states, with one function call. If the number of columns in `x_init` and `x_des` is `q`, then the entries of the three output sequences `x, u, y` are matrices with `q` columns. The `i`th columns are the solution for the initial and end states specified in the `i`th columns of `x_init` and `x_des`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "lqr (generic function with 1 method)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function lqr(A,B,C,x_init,x_des,T,rho)\n",
    "    n = size(A,1)\n",
    "    m = size(B,2)\n",
    "    p = size(C,1)\n",
    "    q = size(x_init,2)\n",
    "    Atil = [ kron(eye(T), C) zeros(p*T,m*(T-1)) ;\n",
    "        zeros(m*(T-1), n*T) sqrt(rho)*eye(m*(T-1)) ]\n",
    "    btil = zeros(p*T + m*(T-1), q)\n",
    "    # We’ll construct Ctilde bit by bit\n",
    "    Ctil11 = [ kron(eye(T-1), A) zeros(n*(T-1),n) ] - [ zeros(n*(T-1), n) eye(n*(T-1)) ]\n",
    "    Ctil12 = kron(eye(T-1), B)\n",
    "    Ctil21 = [eye(n) zeros(n,n*(T-1)); zeros(n,n*(T-1)) eye(n)]\n",
    "    Ctil22 = zeros(2*n,m*(T-1))\n",
    "    Ctil = [Ctil11 Ctil12; Ctil21 Ctil22]\n",
    "    dtil = [zeros(n*(T-1), q); x_init; x_des]\n",
    "    z = cls_solve(Atil,btil,Ctil,dtil)\n",
    "    x = [z[(i-1)*n+1:i*n,:] for i=1:T]\n",
    "    u = [z[n*T+(i-1)*m+1 : n*T+i*m, :] for i=1:T-1]\n",
    "    y = [C*xt for xt in x]\n",
    "    return x, u, y\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We apply the function to the example in §[17.2.1](https://web.stanford.edu/~boyd/vmls/vmls.pdf#subsection.17.2.1)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "A = [ 0.855 1.161 0.667;\n",
    "    0.015 1.073 0.053;\n",
    "    -0.084 0.059 1.022 ];\n",
    "B = [-0.076; -0.139; 0.342 ];\n",
    "C = [ 0.218 -3.597 -1.683 ];\n",
    "n = 3; p = 1; m = 1;\n",
    "x_init = [0.496; -0.745; 1.394];\n",
    "x_des = zeros(n,1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We first plot the open-loop response of VMLS figure [17.4](https://web.stanford.edu/~boyd/vmls/vmls.pdf#figure.17.4) in figure [17.3](#fig3)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
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     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "T = 100;\n",
    "yol = zeros(T,1);\n",
    "Xol = [ x_init zeros(n, T-1) ];\n",
    "for k=1:T-1\n",
    "    Xol[:,k+1] = A*Xol[:,k];\n",
    "end;\n",
    "yol = C*Xol;\n",
    "using Plots\n",
    "plot(1:T, yol', legend = false)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Figure 17.3** <a ind=\"#fig3\"></a>Open-loop response $CA^{t−1}x^{init}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We then solve the linear quadratic control problem with $T = 100$ and $ρ = 0.2$. The result is shown in the second row of VMLS figure [17.6](https://web.stanford.edu/~boyd/vmls/vmls.pdf#figure.17.6) and in figure [17.4](https://web.stanford.edu/~boyd/vmls/vmls.pdf#figure.17.4)."
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   "execution_count": 23,
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   "outputs": [
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     "execution_count": 23,
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   "source": [
    "rho = 0.2;\n",
    "T = 100;\n",
    "x, u, y = lqr(A,B,C,x_init,x_des,T,rho)\n",
    "J_input = norm(u)^2"
   ]
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  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
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     "execution_count": 24,
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   "source": [
    "J_output = norm(y)^2"
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  {
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   "execution_count": 31,
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     "execution_count": 31,
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   ],
   "source": [
    "plot(1:T-1, vcat(u...), legend = true, xlabel=\"t\",\n",
    "ylabel= \"u_t & y_t\")\n",
    "plot!(1:T, vcat(y...))"
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  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Figure 17.4** O<a ind=\"#fig4\"></a>ptimal input and output for $ρ = 0.2$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Linear state feedback control.** To finish the example we implement the state feedback method in VMLS section [17.2.3](https://web.stanford.edu/~boyd/vmls/vmls.pdf#subsection.17.2.3). The plots in figure [17.5](#fig5) reproduce VMLS figure [17.7](https://web.stanford.edu/~boyd/vmls/vmls.pdf#figure.17.7)."
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  },
  {
   "cell_type": "code",
   "execution_count": 40,
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   "source": [
    "# Solve LQ problem with x_init = I, x_des = 0\n",
    "rho = 1.0;\n",
    "xsf, usf, ysf = lqr(A,B,C,eye(n),zeros(n,n),T,rho);\n",
    "K = usf[1];\n",
    "# Simulate over horizon 150\n",
    "TT = 150;\n",
    "Xsf = [x_init zeros(n,TT-1)];\n",
    "for k=1:TT-1\n",
    "    Xsf[:,k+1] = (A+B*K)*Xsf[:,k];\n",
    "end;\n",
    "usf = K*Xsf[:, 1:TT-1];\n",
    "ysf = C*Xsf;\n",
    "# Also compute optimal LQ solution for rho = 1.0\n",
    "x, u, y = lqr(A,B,C,x_init,x_des,T,rho)\n",
    "# Plot the two inputs\n",
    "plot([vcat(u...); zeros(TT-T,1)], label=\"Optimal\", xlabel = \"t\", ylabel = \"u_t\")\n",
    "plot!(usf', label = \"State feedback\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
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      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Plot the two outputs\n",
    "plot_sf_y = plot([vcat(y...); zeros(TT-T,1)], label=\"Optimal\",\n",
    "    xlabel = \"t\", ylabel = \"y_t\")\n",
    "plot!(ysf', label = \"State feedback\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Figure 17.5** <a ind=\"#fig\"></a>The blue curves are the solutions of the linear quadratic control problem for $ρ = 1$. The red curves are the inputs and outputs that result from the constant state feedback $u_t = Kx_t$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 17.3 Linear quadratic state estimation\n",
    "The code for the linear quadratic estimation method is very similar to the one for\n",
    "linear quadratic control."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "lqe (generic function with 1 method)"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function lqe(A,B,C,y,T,lambda)\n",
    "    n = size(A,1)\n",
    "    m = size(B,2)\n",
    "    p = size(C,1)\n",
    "    Atil = [ kron(eye(T), C) zeros(T*p, m*(T-1));\n",
    "        zeros(m*(T-1), n*T) sqrt(lambda)*eye(m*(T-1)) ]\n",
    "    # We assume y is a p x T array, so we vectorize it\n",
    "    btil = [ vcat(y...) ; zeros((T-1)*m) ]\n",
    "    Ctil = [ ([ kron(eye(T-1), A) zeros(n*(T-1), n) ] +\n",
    "            [ zeros(n*(T-1), n) -eye(n*(T-1)) ]) kron(eye(T-1), B) ]\n",
    "    dtil = zeros(n*(T-1))\n",
    "    z = cls_solve(Atil, btil, Ctil, dtil)\n",
    "    x = [ z[(i-1)*n+1:i*n] for i=1:T ]\n",
    "    u = [ z[n*T+(i-1)*m+1 : n*T+i*m] for i=1:T-1 ]\n",
    "    y = [ C*xt for xt in x ]\n",
    "    return x, u, y\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We use the system matrices in §[17.3.1](https://web.stanford.edu/~boyd/vmls/vmls.pdf#subsection.17.3.1) of VMLS. The output measurement data are read from an input file `estimation_data.jl`, which creates a `2 × 100` matrix `ymeas`. We compute the solution for `λ = 103`, shown in the lower-left plot of VMLS figure [17.8](https://web.stanford.edu/~boyd/vmls/vmls.pdf#figure.17.8).\n",
    "\n",
    "The result can be seen in figure [17.6](#fig6)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
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       "  1079.71,1296.56 1133.4,1308.74 1188.37,1320.31 1244.18,1331.32 1300.59,1341.75 1357.42,1351.62 1414.44,1360.95 1471.23,1369.76 1527.61,1378.05 1583.58,1385.86 \n",
       "  1639.16,1393.2 1694.21,1400.09 1748.62,1406.59 1802.23,1412.8 1854.91,1418.77 1906.76,1424.56 1957.72,1430.21 2008.02,1435.75 2057.71,1441.24 2107.11,1446.71 \n",
       "  \n",
       "  \"/>\n",
       "</svg>\n"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ymeas = lq_estimation_data();\n",
    "A = [ eye(2) eye(2); zeros(2,2) eye(2) ];\n",
    "B = [ zeros(2,2); eye(2) ];\n",
    "C = [ eye(2) zeros(2,2) ];\n",
    "n = size(A,1);\n",
    "m = size(B,2);\n",
    "p = size(C,1);\n",
    "T = 100;\n",
    "lambda = 1e3;\n",
    "xest, uest, yest = lqe(A,B,C,ymeas,T,lambda)\n",
    "using Plots\n",
    "scatter(ymeas[1,:], ymeas[2,:], legend = false, axis = false)\n",
    "plot!( [yt[1] for yt in yest], [yt[2] for yt in yest])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Figure 17.6** <a ind=\"#fig\"></a>The circles show $100$ noisy measurements in $2-D$. The solid line is the estimated trajectory $Cx̂_t$ for $λ = 1000$."
   ]
  }
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